13 √(8)=3+√(8)3^2 √(8)^2=3+√(8) ∴(3 √(8) 13 √(8))^2=(3 √(8) (3+√(8)))^2=( 2√(8))^2=4·8=32 ...

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Addition and Subtraction of Like and Unlike Surds

Solve: 3-√8-...

Question

Solve: ${(3 - \sqrt{8} - \frac{1}{3 - \sqrt{8}})}^{2}$

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Solution

$\frac{1}{3 - \sqrt{8}} = \frac{3 + \sqrt{8}}{3^{2} - {\sqrt{8}}^{2}} = 3 + \sqrt{8}$
$∴ {(3 - \sqrt{8} - \frac{1}{3 - \sqrt{8}})}^{2} = {(3 - \sqrt{8} - (3 + \sqrt{8}))}^{2} = (- 2 \sqrt{8})^{2} = 4 \cdot 8 = 32$

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