Estimate the square root of $500 .$

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22.35

20.3

21.4

23.6

answer is A.

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Detailed Solution

Given number is 500.
The two consecutive perfect squares among which

500

lies are

484 (22^{2})

and

529 (23^{2})

.
So, the whole number part of the square root of

500

22 .

The decimal part can be determined by the formula:

decimal part = \frac{Given number – Smaller perfect square}{Greater perfect square – smaller perfect square}

\Rightarrow decimal part = \frac{500 - 484}{529 - 484}

\Rightarrow decimal part = \frac{16}{45}

\Rightarrow decimal part = 0.35

So, the estimated value of the square root of

500

by the approximation method is

22.35 .

Therefore, option (1) is correct.

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