By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.
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.
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☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 102
By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient
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.
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