4 Find the smallest number by which 3645 should be divided so as to get a perfect square Also find the square root of. the number so obtained , 5 Find the square root of 7744 by prime factorization method . 6 Find the square root of 39204 , 7 Find the greatest four digit number which is a perfect square . 8 For each of the following numbers find the smallest number by which we divide it so as to get a perfect square Also. find the square root of the square numbers so obtained . a 37845 b 2800 c 45056, 9 The students of Class VIII of a school donated Rs 2401 for Prime Minister National Relief Fund Each student donated as. many rupees as the number of students in the Class Find the number of students in the Class . 10 There are 500 children in a school For a P T drill they have to stand in such a manner that the number of rows is equal. to number of columns How many children would be left out in this . 11 Using prime factorization find the square root of 7056 . 12 Find the greatest number of 6 digits which is a perfect square plot . 13 Find the square root of 7 upto 3 decimal places . 14 Find the square root of 2 correct to 3 decimal places . 15 Find the square root of 0 00126736 by division method . 16 A school collected Rs 2304 as fees from its students If each student paid as many rupees as there were students in the. school how many students were there in the school . 17 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows . Find the number of rows and the number of plants in each row . 18 10404 students are sitting in a lecture room in such a manner that there are as many students in a row as there are. rows in a lecture room How many students are there in each row of a lecture room . 19 Find a Pythagorean triplet corresponding to n 5 . 20 Find the least number of 5 digits which is a perfect square . 21 Find the approximate length of the side of a square whose area is equal to the area of a rectangle with sides. 15cm and 16cm , 22 The area of a square field is 2 square metres Find the length of the side of the field . 4Marks Questions, 1 Find the square of 2 5 correct upto 3 decimal places . 2 Find the square root of 2 correct to 3 decimal places . 3 Find the square root of 90 by Estimation method . 4 The area of a square field is 5184 m A rectangular field whose length is twice of its breadth has its. perimeter equal to the perimeter of the square field Find the area of the rectangular field . 5 The cost of leveling a square field at Rs 15 per square metre is Rs 19935 Find the cost of fencing the field at. Rs 22 per metre , 125, 6 If 2 1 414 3 1 732 5 2 236 find the value of i 72 48 ii . 7 The product of two numbers is 1296 If one of the number is 16 times other find the number . 8 Find the three numbers in the ratio 2 3 5 the sum of whose square is 608 . CH 2 CUBES AND CUBE ROOT, 1Mark Questions,1 Show that 46656 is a perfect cube . 2 What is the ones digit in the cube of 38 , 3 Find the sides of a cubical box whose volume is 64 cm . 4 How many perfect cubes are there between 1 and 1000 . 5 Is the cube of 4913 an odd number Why ,6 Volume of a cube is 9261 cm Find its edge . 7 Find the cube root of 0 064 , 3 3,8 1km cm , 9 The cube of any multiple of 3 is always divisible by . 10 Find the cube of 0 2 ,11 Is 9000 a perfect cube . 12 Write all the digits that would appear as the last digits of their respective cubes . 2Marks Questions, 1 By which smallest number should 42592 be divided so that the quotient is a perfect cube . 2 By which smallest number should 704 be divided to obtain a perfect cube . 3 Show that 384 is not a perfect cube , 4 By which smallest number should 648 be multiplied so that the product is a perfect cube . 5 Find the number whose cube is 27000 ,6 Find the cube root of 3375 . 7 Find the cube root of the number 614125 using prime factorization method . 8 Find the cube of square of 0 2, 3Marks Questions. 1 Find the smallest natural number by which 392 must be multiplied so that the product is a perfect cube . 2 Find the cube root of 27 x 2744 , 3 Show that 0 001728 is a cube root of a rational number. 4 Multiply 10584 by the smallest number so that the product is a perfect cube . 5 The volume of a cube is 4096 cu m Find the length of the side of cube . 6 Find the cube root of the number 110592 by the estimation method . 7 Evaluate , 8 Find the volume of a cube one face of which has an area of 81 m . 9 If the surface area of a cube is 486 cm find its volume . 10 Find volume of a cube whose surface area is 96 cm . 11 Find the number by which 68600 must be multiplied to get a perfect cube . 12 What is the smallest number by which 288 must be multiplied so the product is a perfect cube . 13 Show that if a number is doubled then it cube becomes eight times the cube of the given number . 14 Which smallest natural number should divide 1188 so that the quotient is a perfect cube . 15 Is 292 a perfect cube If not find the smallest natural number by which it must be multiplied so that the product is a. perfect cube , 4 Marks Questions, 1 Find the smallest number which multiplied with 3600 will make the product a perfect cube Further find the cube root of. the product , 2 Find the approximate length of the side of a cube whose volume is equal to a cuboid having dimensions 100m 11m and. 3 Divide the number 52728 by the smallest number so that the quotient is a perfect cube Also find the cube root of the. 4 Prove that if a number is tripled then its cube is 27 times the cube of the given number . ,5 Evaluate X, , 6 Difference of two perfect cube is 189 If the cube root of the smaller of the two number is 3 find the cube root of the. larger number , 7 Three numbers are in the ratio 1 2 3 and the sum of their cubes is 4500 Find the numbers . 8 Find the area of one face of a cube if its volume is 512 cm . CH 3 EXPONENTS AND RADICALS, 1Mark Questions, 1 1 1. 1 Evaluate 1 2 1 3 , 2 What is the value of 1 1 , 3 What is the reciprocal of 3 4 . 4 What is the multiplicative inverse of 2 , 6 Find x if 2 3. 7 What is the value of 8 , 8 The value of 512, 2 . 9 Find 10 if 10 25, 3 1 3, 10 Find the value of 5 x . 5 6, 11 Simplify 2 2 , 12 Express 4 as a power with base 2 . 13 Find the value of 2 3 , 2Marks Questions, 7 5, 1 Simplify 5 8 x 8 5 . m 3 5, 2 Find the value of m for which 5 5 5, 3 Find m if 3 92 3m 3 3. 6 7, 3 Compare 7 X 10 and 129 X 10, 4 2 3 4 1 3, 4 Simplify . 3 3, 5 7 8 5, 5 Evaluate , 8 5, 0 1 2, 6 Find value of 3 4 2. 10 5, 7 Simplify 4 x 4 , 1 2 3 1, 8 Evaluate 5 x 8 2 x 10 . 9 Find the value of m for which 6 6 6 , 5 5, 10 Simplify 3 x 5 3 . 11 The size of a plant cell is 0 00001275 m express it in standard form . 4 1, 12 Simplify 13 3 13 3, 1 2 1 3 1 4, 13 Find the value of . 4 3 2, 14 Simplify , 3Marks Questions, xb x c c a b x a a b c. 15 Simplify , xc xa xb, 16 If the thickness of a paper sheet is 0 0016 cm find the thickness of 100 sheets Express the answer in standard. form 4 , 2 4, 27 3 27 3, 17 Evaluate , 125 125, 1 4. 18 Evaluate 625 2, 19 If a 2 and b 3 then find the value of ab ba. 2 1 4,20 Find value of 273 273 y 33y 27 3, 3 2 1, 7 2 7 3 7 3 7 2 x. 21 Find x 8 8, 1 1 1 1 x,23 Find the value of x so that 2 4 6 8 1. 24 The cells of a bacteria double in 30 minutes A scientist begins with a single cell How many cells will be there after 12. CH 4 DIRECT AND INVERSE VARIATION, 1Mark Questions. 1 Do x and y vary directly in the given table , X 4 20 30 40 60 80. Y 2 8 10 15 20 25, 2 If y is directly proportional to 1 x and x 2 when y 20 what is the value of x when y 1 25 . 3 If x and y vary inversely and y 45 Find x when constant of variation 9. 4 What do you mean by direct and inverse variation . 5 If x 5y then x and y vary with each other , 6 If xy 10 then x and y vary with each other . 7 x and y are in direct variation If y 10 then x 5 Find the value of y when x 10 . 8 Time taken to cover a distance by a car and speed of the car are said to be in variation . 9 x and y are in inverse proportion If y 15 then x 3 find the value of y when x 9 . 10 Time taken to cover a distance by a car and speed of the car are said to be in variation . 3Marks Questions, 1 If 12m of a uniform iron rod weights 42 kg What will be the weight of 6m of same rod . 2 A train 360m long is running at a speed of 45 km hr What time will it take to cross a 140m long. 3 A train 210m long took 12 seconds to pass a 90 m long tunnel Find the speed of the train . 4 68 boxes of certain commodity require a shelf length of 13 6 m How many boxes of the same. commodity would occupy a shelf length of 20 4 m , 5 11 men can dig 6 75m m long trench in one day How many men should be employed for digging. 27m long trench of the same type in one day , 6 A worker is paid Rs 210 for 6 days work If his total income of the month is Rs 875 for how many. days did he work , 7 If 12m of a uniform iron rod weights 42 kg What will be the weight of 6m of same rod . 8 If the speed of a train be 92 4 km h how many meters would it cover in 20 minutes. 9 5 bags of rice weigh 150 kg How many such bags of rice will weigh 900 kg . 10 If 20 men can reap a field in 8 days then 16 men will reap the same field in how many days . 11 6 pumps working together empty a tank in 28 minutes How long will it take to empty the tank if 4. pumps working together , 3 1, 12 Walking at the th of his usual speed a man is late by 2 hours Find his usual time . 4 2, 13 If a train 120m long crosses a man in 15 seconds Then find the speed of the train . 14 A train 210m long took 12 seconds to pass a 90m long tunnel Find the speed of the train . 4Marks Questions, 1 120 men had food provisions for 200 days After 5 days 30 men die due to an epidemic How long. will the remaining food last , 2 A car can finish a certain journey in 10 hours at the speed of 48km hr By how much should its speed. be increased so that it may take only 8 hours to cover the same distance . 3 In a hostel of 50 girls there are food provisions for 40 days If 30 more girls join the hostel how long. will these provisions last , 4 A train 400m long is running at a speed of 72km hr How much time does it take to cross a telegraph. 5 If 5 men or 7 women can earn Rs 875 per day how much would 10 men and 5 women earn per day. 6 The cost of 16 packets of salt each weighing 900 g is Rs 84 Find the cost of 27 packets of salt each. weighing 1kg , 7 If 3 persons can weave 168 shawls in 14 days how many shawls will be woven by 8 persons in 5. 8 If the cost of transporting 160kg of goods for 125 km is Rs 60 What will be the cost of transporting. 200kg of goods for 400km , 9 6 oxen and 8 cows can graze a field in 28days How long would 9 oxen and 2 cows take to graze the. same field , 10 6 men working 8 hours a day earn Rs 8400 per week What will be the earning per week of 9. men who work for 6 hours a day , 11 A motor boat covers 20 km in 4 hours What distance will it cover in7 hours speed remaining the. 12 Find a in the following table When, X 2 5, Y 10 a. i x y vary directly ii x y vary inversely, 13 A train is moving at a uniform speed of 72 km h How far will it travel in 25 minutes Find the time. required to cover a distance of 216 km , 14 A school has 8 periods a day each of 45 minutes duration How long would each period be if the. school has 9 periods a day assuming the number of school hours to be the same . 15 A garrison of 500 men had provision for 60 days A reinforcement of 500 men arrived the food will. now last for how many days , 16 A fort had provision for 300men for 90days After 20days 50men left the fort How long would the. food last at the same rate , 17 A certain number of men finish a piece of work in 100 days If however there were 10 men less it. would take 10 days more for the work to be finished How many men were these originally . 18 How long a train 120m long take to clear a platform 130m long if its speed is 50km h . 19 A shopkeeper has enough money to buy 40 books each costing Rs125 How many books he can buy. if he gets a discount of Rs25 on each book , 20 Ravi starts for his school at 8 20a m on his bicycle If he travels at a speed of 10 km hr then he. reaches his school late by 8 minutes but on travelling at 16 km hr he reaches the school 10 minutes. early At what time does the school start , 21 Ms Amisha has to drive from Jhareda to Ganwari She measures a distance of 3 5 cm between these. village on the map What is the actual distance between the villages if the map scale is 1 cm 10 km . CH 5 PROFIT LOSS AND DISCOUNT, 1Mark Questions, 1 The marked price of a book is Rs 250 and 5 discount is given Find the selling price of the. 2 By selling a bag for Rs180 a shopkeeper loses Rs 20 Find the cost price of the bag . 3 C p of a pair of shoes is Rs350 If VAT is Rs 50 find the S P of the a pair of shoes . 4 If S P of a shirt is Rs 500 and loss is Rs 50 Find the C P of the shirt . 2Marks Questions, 1 If by selling an article for Rs100 a man gains Rs15 then find his gain percent . 2 Marked price of a frock is Rs220 A discount of 20 is announced on it What is the amount of disco. DAV PUBLIC SCHOOL JHARSUGUDA CLASS VIII CHAPTER 1 TO 16 CH 1 SQUARES AND SQAURE ROOTS 1Mark Questions 1 The least numbers which must be subtracted from 4360 to make it a perfect square is

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