SQUARE ROOTS AND CUBE ROOTS

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1 9 SQUARE ROOTS AND CUBE ROOTS. Find the smallest natural number by which the following numbers must be multiplied to make them a perfect square: (i) 68 (ii) 8 Ans. (i) Since the factor does not have its pair. So, the given number must be multiplied by. (ii) 8 Since the factor does not have its pair, So, the given number must be multiplied by Find the smallest natural number by which the following number must be divided to make them a perfect square: (i) 59 (ii) 64 Ans. (i) Since the factor does not have its pair, so, the given number must be divided by Math Class VIII Question Bank

2 (ii) 64 Since the factor i.e. 6 does not have its pair, so, the given number must be divided by 6.. What least number must be subtracted from the following numbers to make them a perfect square? (i) 894 (ii) 0 Ans. (i) The square root of 894 can be calculated as: Hence, we will have to subtract 98. (ii) The square root of 0 can be calculated as: Hence, we will have to subtract Math Class VIII Question Bank

3 4. What least number must be added to the following numbers to make them perfect squares? (i) 568 (ii) 8000 Ans. (i) The square root of 568 can be calculated as: Hence, we will have to add (6) (ii) The square root of 8000 can be calculated as: Hence, we will have to add (90) Find the square root of: (i) 584 (ii) 6 9 (iii) (iv) 6.06 (v) Ans. (i) Math Class VIII Question Bank

4 (ii) (iii) (iv) Math Class VIII 4 Question Bank

5 (v) Find the value of the following: (i) 85 6 (iii) (.) (.) (ii) Ans. (i) (ii) (iii) (.) (.) (. +.)(..) ( )( ) Math Class VIII 5 Question Bank

6 . Find the value of 565 and hence evaluate Ans Thus and Hence, Evaluate : (i) (ii) 4 4 (iii) Ans. (i) (ii) 4 4 (iii) Math Class VIII 6 Question Bank

7 ( ) ( ) ( ) A man, after a tour, finds that he had spent every day as many rupees as the number of days he had been on tour. How long did his tour last, if he had spent in all Rs,96? Ans. Let the number of days he had spent be x Number of rupees spent in each day x Total money spent x x x,96 Thus x 96 x x 4 9 x 6 0. A society collected Rs 9,6, each member contributed as many rupees as there were members in the society. Find the number of members. Ans.Let the number of members be x. Money collected by each member be x. Thus total money collected x x x 96 x 96 x x x 96 Hence, number of members are 96.. A basket contains 5 flowers. A man goes for worship and puts as many flowers in each temple as there are temples in the city. Math Class VIII Question Bank

8 If the man needs 0 baskets of flowers, find the number of flowers that he puts in each temple. Ans.Let the number of flowers put in each temple be x. Thus total number of flowers used x x x 5 0 x 500 x x 50 Hence, the number of flowers put it each temple is 50.. Find the square root of the following numbers by division method : (i) 444 (ii) (iii) Ans. (i) 444 (ii) (iii) Math Class VIII 8 Question Bank

9 . Find the square root of correct to significant figures. Hence find the value of + correct to decimal places. Ans.. Now ( ) ( ) ( ) ( ) ( + ) Hence,. 4. Find the least number which must be subtracted from 58 to obtain a perfect square. Find this perfect square and its square root. Ans The number which is to be subtracted and perfect square and square root Math Class VIII 9 Question Bank

10 5. Find the least number which must be subtracted from to obain a perfect square. Find the perfect square and its square root. 08 Ans Hence, the number which must be subtracted 5 and perfect square and square root Find the least number which must be added to 60 to obtain a perfect square. Find the perfect square and its square root. Ans must be added in order to get a perfect square. Thus the number to be added 8 Perfect square and square root 9. Find the least number which must be added to to make it a perfect square. Find this perfect square and its square root. Ans Math Class VIII 0 Question Bank

11 must be added to get a perfect square Thus number to be added 44 Perfect square and square root 8. Find the greatest number of six-digit which is a perfect square. Find the square root of the number. Ans. The greatest 6-digit number Thus the required 6-digits number which is a perfect square Hence, square root of the number is The students of a class arranged a picnic. Each student contributed as many rupees as the number of students in the class. If the total contribution is Rs 60, find the strength of the class. 5 Ans.Total contribution Rs Let number of students be x Contribution of each students Rs x 5 Thus Rs x x x x 60 x 5 0 Hence, number of students are 5 0. Test whether the given number is a perfect cube or not : (i) 80 (ii) 0584 Ans. (i) 80 5 Making a groups of, its factors are not in triplet. Hence, it is not a perfect cube Math Class VIII Question Bank

12 (ii) 0584 Thus its factors, is not in triplet. Hence, it is not a perfect cube.. Find the smallest number by which 99 must be multiplied so that the product is a perfect cube. Ans.Resolving 99 into prime factors, we get 99 To make the above number a perfect cube we have to multiply it by Find the smallest number by wihch 888 must be divided so that the quotient is a perfect cube. 888 Ans.Writing 888 as a product of prime factors, we get from above it is clear that the smallest 69 number to divide the given number to make it perfect cube is 4 Hence, the required number is 4.. Find the cube root of : (i) 4088 (ii) (iii) (iv) 4.85 Math Class VIII Question Bank

13 Ans. (i) 4088 (ii) ( ) ( ) Thus, ( ) (iii) Math Class VIII Question Bank

14 (iv) Multiply 656 by the smallest number so that the product is a perfect cube. Also find the cube root of the product. 656 Ans. Splitting 656 into prime factors, we have The required number is which is to be 4 multiplied to 656, so that the product is a 8 perfect cube. Hence the cube root of the product Divide 59 by the smallest number so that the quotient is a perfect cube. Also find the cube root of the quotient. Ans.First of all, we find the prime factorisation of We note that the prime factors and occur thrice while prime factors and occur twice and once. Therefore, the smallest number by which the given number must be divided so that the quotient is a perfect cube is i.e. 6. Also the quotient 59 6 Now 6 ( ) ( ) Hence, 6 6. Math Class VIII 4 Question Bank

Cubes and Cube Roots

CUBES AND CUBE ROOTS 109 Cubes and Cube Roots CHAPTER 7 7.1 Introduction This is a story about one of India s great mathematical geniuses, S. Ramanujan. Once another famous mathematician Prof. G.H. Hardy