Question

4. Find the least number of four digits which is a perfect square.
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Answer 1

Step-by-step explanation:

1024 is the least no. of four digits which is a perfect square of 32

Answer 2

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$\huge \mathfrak \blue { \underline {1024}}$

The least number of four digits which is a perfect square is

31 ² = 961

32 ² = 1024

33 ³ = 1089

34 ² = 1156

Least number of four digits = 1000.

The smallest four-digit number is 1000 but square root of 1000 gives the value 31.62 which 1000 is not a perfect square.

In order to obtain the smallest 4-digit perfect square, numbers higher than 1000 must be checked. The possibility is the square of 32 as the square of 31 will be less than 1000.

(32)2 is more than 1000 by 24.

So, the least number to be added to 1000 is 24.

1000 + 24 = 1024

Therefore, the smallest four digit number which is a perfect square is 1024.

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I hope my answer helps you...

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