Question

find the square root of 9 + 2 root 20​

Answer 1

The value of  square root of ${9+2\sqrt{20} }$ is $\sqrt{5} +\sqrt{4}$.

Explanation:

Given:

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

To Find:

The value of  square root of ${9+2\sqrt{20} }$ .

Solution:

As given,$\sqrt{9+2\sqrt{20} }$.

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

                  $=5+4+2\sqrt{5\times4}$

                  $=9+2\sqrt{20}$

It means we can write $9+2\sqrt{20}=(\sqrt{5} +\sqrt{4} )^{2}$

The value of $\sqrt{9+2\sqrt{20} }$

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

                 $=\sqrt{5} +\sqrt{4}$

Thus, the value of  square root of ${9+2\sqrt{20} }$ is $\sqrt{5} +\sqrt{4}$.

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Answer 2

Answer:

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

Explanation:

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

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

$9 + 2\sqrt{20}$ 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 square root of 9 + 2root 20.

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

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

Final answer:

Hence, $(\sqrt{5}+\sqrt{4} )^2$ this is the required answer.

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