Question

Solve this question guys..​

Answer 1

Given To Rationalise:

• $\sf \dfrac{ \sqrt{8} }{4 + 2 \sqrt{2} }$

Solution:

Given,

$\sf = \dfrac{ \sqrt{8} }{4 + 2 \sqrt{2} }$

$\sf = \dfrac{ \sqrt{4 \times 2} }{2(2 +\sqrt{2} )}$

Cancel out 2,

$\sf = \dfrac{2 \sqrt{2} }{2(2 +\sqrt{2} )}$

$\sf = \dfrac{\sqrt{2} }{(2 +\sqrt{2} )}$

Cancel out √2,

$\sf = \dfrac{\sqrt{2} }{ \sqrt{2} ( \sqrt{2} +1)}$

$\sf = \dfrac{1}{\sqrt{2} +1}$

Rationalise,

$\sf = \dfrac{1}{\sqrt{2} +1} \times \dfrac{ \sqrt{2} - 1 }{ \sqrt{2} - 1}$

$\sf =\dfrac{ \sqrt{2} - 1 }{ ( \sqrt{2} + 1)(\sqrt{2} - 1)}$

$\sf =\dfrac{ \sqrt{2} - 1 }{2 - 1}$

$\sf =\dfrac{ \sqrt{2} - 1 }{1}$

$\sf =\sqrt{2} - 1$

Hence, result = √2 - 1

= 1.414 - 1

= 0.414

Answer:

• Result = √2 - 1

Answer 2

Answer is in the attachment