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Find the smallest number by which must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
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Q. Find the smallest number by which must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
- Factorize : To find the smallest number by which must be divided to make it a perfect square, we first need to factorize into its prime factors.
- Identify Prime Factors: We can see that has the prime factors and . For a number to be a perfect square, all the prime factors must be in pairs. In the prime factorization of , the number is not in a pair.
- Divide by : To make a perfect square, we need to divide it by , because this will leave us with only the prime factor , which is already in pairs (four pairs of ).
- Find Square Root: Now, we need to find the square root of the resulting number, which is . Since is a perfect square (), its square root will be the product of pairs of the prime factor.Square root of
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