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Question

Is 1800 a perfect square? If not, find the smallest number by which it can be divided to make it a perfect square.

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Solution

The prime factoristion of 1800 is :1800 = 2×2×2×3×3×5×5Here, prime factor 2 does not ocurr in a pair, so 1800 is not a perfect square.Now, to make 1800 a perfect square, it must be divided by 2.Now, 1800 ÷ 2 = 2×2×2×3×3×5×52 = 900 a perfect square numberNow, 900 = 2×2×3×3×5×5900 = 2×2×3×3×5×5 = 2×3×5 = 30

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