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प्रश्न
By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.
उत्तर
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 2 × 3 i.e. 6, then
New number = `216/6` = 36
Taking one factor from each, we get square root of new number (quotient)
= 2 × 3
= 6
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