Question

find the squareroot of 10+2root24

Answer 1

$\textbf{ Hello Mate! }$

$= \sqrt{10 + 2 \sqrt{24} }$

Let's now think s little deep.

Think of two numbers whose sum is 10 and product is 24. Here we get two numbers : 6 and 4.

$= \sqrt{ { \sqrt{6} }^{2} + { \sqrt{4} }^{2} + 2 \times \sqrt{6} \times \sqrt{4} } \\ {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ = \sqrt{ { (\sqrt{6} + \sqrt{4} )}^{2} } \\ = \sqrt{6} + \sqrt{4}$

But don't end up here, we know that root 4 = 2

$= 2 + \sqrt{6}$

Have great future ahead!

Answer 2

$<u><b>Hii <b><u>$

Here is your answer !!

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$\sqrt{10 + 2 \sqrt{24} }$

Expanding it , We get

$= > \sqrt{ { \sqrt{6} }^{2} + { \sqrt{4} }^{2} + 2 \times \sqrt{6} \times \sqrt{4} }$

USING the formula ,

$(a + b) = {a}^{2} + {b}^{2} + 2ab$

$= > \sqrt{ {( \sqrt{6} + \sqrt{4} ) }^{2} } \\ \\ = > \sqrt{6} + \sqrt{4} \\ \\ = > \sqrt{6} + 2 \: \: \: ans$

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THANK YOU !!!