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3600 = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 5. To make it a perfect cube, the given number must be divided by 2 x 3 x 3 x 5 x 5 = 450
Solution: Given, the number is 3600. We have to find the smallest number by which 3600 should be multiplied so that the quotient is a perfect cube and the cube root of the quotient. Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Using prime factorisation, So, 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 We observe that 2 occurs once and 3,5 occur twice. 3600 must be multiplied by 2 × 2 × 3 × 5 to make it a perfect cube. 2 × 2 × 3 × 5 = 60 So, 3600 × 60 = 216000 Therefore, the smallest number by which 3600 must be multiplied is 60. Cube root is an inverse operation of a cube. 216000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5 So, ∛216000 = ∛(2³ × 2³ × 3³ ×5³) = 2 × 2 × 3 × 5 = 60 Therefore, the cube root of the quotient is 60. ✦ Try This: By what smallest number should 2500 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient. ☛ Also Check: NCERT Solutions for Class 8 Maths NCERT Exemplar Class 8 Maths Chapter 3 Problem 102 Summary: The smallest number by which 3600 should be multiplied so that the quotient is a perfect cube is 60. The cube root of the quotient is 60. ☛ Related Questions: |