By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.
Solution:
Given, the number is 216.
We have to find the smallest number by which 216 should be divided so that the quotient is a perfect square and the square 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, 216 = 2 × 2 × 2 × 3 × 3 × 3
We observe that 2 and 3 occur without a pair.
216 must be divided by 2 × 3
2 × 3 = 6
So, 216 / 6 = 36
This implies the quotient is a perfect square.
Therefore, the smallest number by which 216 must be divided is 6.
Square root is an inverse operation of a square.
So, √36 = √(6)²
= 6
Therefore, the square root of the quotient is 6.
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☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 101
By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient
Summary:
The smallest number by which 216 should be divided so that the quotient is a perfect square is 6. The square root of the quotient is 6.
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