Find the least number of four digits which is a perfect square.

Question:

Find the least number of four digits which is a perfect square. Also find the square root of the number so obtained.

Solution:

Smallest number of four digits =1000

Using the long division method:


1000 is not a perfect square.

By the long division method, the obtained square root is between 31 and 32.

Squaring the next integer (32) will give us the next perfect square.

$32^{2}=1024$

Thus, 1024 is the smallest four digit perfect square.

Also, $\sqrt{1024}=32$

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