Question

find the square root of 9 + 2 root 20​

Answer 1

Answer:

The square root of $\sqrt{9 + 2\sqrt{20}}$ is $(\sqrt{5} + \sqrt{4} )^$

Step-by-step explanation:

Explanation:

Given in the question that, $9 + 2\sqrt{20}$

According to the question we need to find out the square root of $9 + 2\sqrt{20}$.

And $9 + 2\sqrt{20}$ can be written as

⇒$9 + 2\sqrt{20}$ = $(\sqrt{5})^2 + (\sqrt{4} )^2+ 2 .(\sqrt{5} )\sqrt{4}$

⇒ $9 + 2\sqrt{20}$ =   $(\sqrt{5} + \sqrt{4} )^2$

Verify:

Where $(\sqrt{5} + \sqrt{4} )^2$ = $(\sqrt{5})^2 + (\sqrt{4} )^2+ 2 .(\sqrt{5} )\sqrt{4}$

⇒ $(\sqrt{5} + \sqrt{4} )^2$ = 5 + 4 + 2$\sqrt{20}$

⇒$(\sqrt{5} + \sqrt{4} )^2$ = 9 + 2$\sqrt{20}$

Now, according to the question, the square root of  $9 + 2\sqrt{20}$

⇒ $\sqrt{9 + 2\sqrt{20}}$ = $\sqrt{(\sqrt{5} + \sqrt{4} )^2}$

⇒  $\sqrt{9 + 2\sqrt{20}}$  =   $(\sqrt{5} + \sqrt{4} )^$

Final answer:

Hence, the square root of $\sqrt{9 + 2\sqrt{20}}$ is $(\sqrt{5} + \sqrt{4} )^$

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Answer 2

Answer:

The square root of the given equation is $(\sqrt{5} +\sqrt{4} )$

Explanation:

Given:

Equation - $9+2\sqrt{20}$

To Find:

The square root of the equation i.e. $9+2\sqrt{20}$

Solution:

$9+2\sqrt{20}$(Given)

We need to find it's square root, making it as $\sqrt{9+2\sqrt{20} }$

Changing the equation by splitting it,

$9+2\sqrt{20} = (\sqrt{5} )^{2} + (\sqrt{4} )^{2} + 2(\sqrt{5} )(\sqrt{4} )$

$9+2\sqrt{20} = (\sqrt{5} )^{2} + (\sqrt{4} )^{2} + 2*\sqrt{5}*\sqrt{4}$

$9+2\sqrt{20} = (\sqrt{5} +\sqrt{4} )^{2}$

According to the question and the earlier equation we need to solve or simplify, $\sqrt{9+2\sqrt{20} }$

Thus, $=\sqrt{ (\sqrt{5} +\sqrt{4} )^{2}}$

$\sqrt{9+2\sqrt{20} }=\sqrt{5} +\sqrt{4}$.

Therefore, the square root of the equation provided to us is $\sqrt{5} +\sqrt{4}$

Verification:

$(\sqrt{5} +\sqrt{4})^2=(\sqrt{5} )^2+(\sqrt{4} ^2)+2*\sqrt{5} *\sqrt{4}$

$(\sqrt{5} +\sqrt{4})^2=5+4+2\sqrt{20}$

$(\sqrt{5} +\sqrt{4})^2=9+2\sqrt{20}$

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