Question

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$\sqrt{5 - \sqrt{2} + \sqrt{18 + 8 \sqrt{2} } }$
plz answer it!!!!

Answer 1

The answer is given below :

Now, 18 + 8√2

= 16 + 8√2 + 2

= 4² + (2 × 4 × √2) + (√2)²

= (4 + √2)²,

using the identity
(a + b)² = a² + 2ab + b²

Now, √(18 + 8√2)

= √{(4 + √2)²}

= 4 + √2,
taking the positive value

So, √{5 - √2 + √(18 + 8√2)}

= √(5 - √2 + 4 + √2)

= √9

= ± 3

I hope that it helps you.

Answer 2

$\bf HELLO \: \: DEAR,$


$\bf \: \sqrt{5 - \sqrt{2} + \sqrt{18 + 8 \sqrt{2} } }$


$\bf \sqrt{5 - \sqrt{2} +\sqrt{18 + 8\sqrt{2}}} \\ \\ \bf \sqrt{5 - \sqrt{2} +\sqrt{16 + 2 + 2(4)\sqrt{2}}} \\ \\ \bf \sqrt{5 - \sqrt{2} +\sqrt{(4 + \sqrt{2})^{2}}} \\ \\ \bf \sqrt{5 - \sqrt{2} + 4 + \sqrt{2}}$


$\bf \sqrt{5 + 4} \\ \\ = \bf \sqrt{9} \\ \\ = \bf +_- \: 3$



$\underline{\bf I \: \: HOPE \: \: ITS \: \: HELP \: \: YOU \: \: DEAR, \: \: THANKS}$