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If $\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}$ , find K...

If $\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}$ , find K

A.

-2

B.

-1

C.

1

D.

2

View answer & explanation

Correct answer is D

$\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}$

$\sqrt{50} - \frac{2}{\sqrt{2}}$ = K $\sqrt{8}$

= $\sqrt{2} \times 25 - \frac{2}{\sqrt{2}}$

= K $\sqrt{4 \times 2}$

$\frac{5\sqrt{2}}{1} - \frac{2}{\sqrt{2}}$ = 2K $\sqrt{2}$

$\frac{5\sqrt{4} - 2}{\sqrt{2}} = 2K\sqrt{2}$

$\frac{10 - 2}{\sqrt{2}} = 2K \sqrt{2}$

$\frac{8}{\sqrt{2}} = \frac{2K\sqrt{2}}{1}$

= 2k $\sqrt{2} \times \sqrt{2}$ = 8

2k $\sqrt{4}$ = 8

2k x 2 = 8

4k = 8

k = $\frac{8}{4}$

k = 2

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