Squeaky roots

pls help me to find the value of this sum please,I've been trying a lot and hence I need your help

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@erica phillips I think this question is from FTRE. The solution is...

$\large \begin{aligned} \sqrt{2} \times \sqrt{3+\sqrt{2}+\sqrt{3}+\sqrt{6}}-1-\sqrt{2}-\sqrt{3} \\ &=\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}-1-\sqrt{2}-\sqrt{3} \\ &=1+\sqrt{2}+\sqrt{3}-1-\sqrt{2}-\sqrt{3} \\ &=0 \end{aligned}$

The main thing to note here was that the thing in square root was in fact a square...! Because that would only simplify your task.

Vilakshan Gupta - 3 years, 5 months ago

how did u multiply 2^1/2 with all the nos. under the square root

erica phillips - 3 years, 5 months ago

It is the basic of maths...! Well i guess , you know that $2\sqrt{2}=\sqrt{8}$ ? If you know this,then you shouldn't have any problem in the solution.If you don't know this....then I can't help.

Vilakshan Gupta - 3 years, 5 months ago

$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$

Venkatesh G - 2 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$