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Question

Question 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.


Solution

Prime factors of 216=2×2×2×3×3×3
Grouping the factors into pairs of equal factors, we get
216=2×2×2×3×3×3
We find that there is no prime factor to form a pair with 2 and 3.
Therefore, we must divide the number by 6, so that the quotient becomes a perfect square.
If we divide the given number by 6, then
New number =2166=36
Taking one factor from each, we get square root of new number (quotient)
=2×3=6


Mathematics
NCERT Exemplar
Standard VIII

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