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How do you find the square root of 1728?

Answer
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Hint:In the given question, we have been asked to find the simplified form of the square root of an even natural number. To solve this question, we just need to know how to solve the square root. If the number is a perfect square, then it will have no integer left in the square root. But if it is not a perfect square, then it has at least one integer in the square root.

Complete step by step answer:
The given number whose simplified form is to be found in the square root of 1728, or we have to evaluate the value of 1728.
First, we find the prime factorization of 1728 and club the pair(s) of equal integers together.
2|17282|8622|4322|2162|1082|543|273|93|3|1
Hence, 1728=2×2×2×2×2×2×3×3×3=22×22×22×32×3=242×3
Hence, 1728=(24)2×3=243

Thus, the simplified form of 1728 is 324.

Note: When we are calculating such questions, we find the prime factorization, club the pairs together, take them out as a single number and solve for it. This procedure requires no further action or steps to evaluate the answer. It is a point to remember that a perfect square always has an even number of factors.
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