Question

Find the square root of 410 by estimation​

Answer 1

Answer:

Refer the above attachment

Answer 2

Hello...

Answer...

The perfect square near to 410 are 400. and 441.

I. e. 400 < 410 < 441

{20}^{2} < 410 < {21}^{2}20

2

<410<21

2

We guess the answer is between 20 and 21

Let us try with 20.3 as 20 < 20.3 < 21

But

\begin{gathered}( {20.3)}^{2} = 412.09 > 410 \\ \\ i.e \: \: \: {20}^{2} < 410 < ( {20.3)}^{2} \end{gathered}

(20.3)

2

=412.09>410

i.e20

2

<410<(20.3)

2

Let us try. 20.2 We

\begin{gathered}20.2 \times 20.2 = 408.04 \\ \\ 408.04 < 410 < 412.09 \\ \\ ( {20.2})^{2} < 410 < ( {20.3)}^{2} \\ \\ We \: take \: \sqrt{410 \: } \: \: \: as \: \: 20.2 \: \: \: approximately.\end{gathered}

20.2×20.2=408.04

408.04<410<412.09

(20.2)

2

<410<(20.3)

2

Wetake

410

as20.2approximately.

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