Question

Hey mate!!

Find the square root of :-
$3 + \sqrt{2}$

Please explain also.
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Answer 1

$3 + \sqrt{2}$

We have To Find Square Root Of it.

Square Root of a=√a

So Write Given In Form of √

$\sqrt{3 + \sqrt{2} }$

Let

$\sqrt{3 + \sqrt{2} } = \sqrt{x} + \sqrt{y} \\ \\ 3 + \sqrt{2} = ( \sqrt{x} + \sqrt{y} ) {}^{2} \\ \\ 3 + \sqrt{2} = { \sqrt{x} }^{2} + { \sqrt{y} }^{2} + 2 \sqrt{xy} \\ \\ 3 + \sqrt{2} = x + y + 2 \sqrt{xy}$

Comparing Both sides.

We get.

x+y=3

2√(xy)=√2

$2 \sqrt{xy} = \sqrt{2} \\ \\ \sqrt{xy} = \frac{1}{2} \times \sqrt{2} \\ \\ xy = (\frac{1}{2} \times \sqrt{2} ) {}^{2} \\ \\ xy = \frac{1}{4} \times 2$

X×Y=1/4×2

X=1/4

Y=2

Square Root was

√x+√y

√1/4+√2

1/2+√2

$\huge \boxed {\sqrt{3 + \sqrt{2} } = \frac{1}{2} + \sqrt{2} }$