Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\sqrt{\frac{2+\sqrt 2}{2-\sqrt 2}}=$	A. $2\, \sqrt 2$
	B. $2\, \sqrt 2 - 1$
	C. $\sqrt 2 + 1$
	D. $\sqrt{2+3\sqrt2}$
	E. $2\sqrt{3+2\sqrt2}$
	F. $\frac{\sqrt 2 + \sqrt[4]{2}}{\sqrt 2-\sqrt[4]{2}}$

[ 3-7500 - op net sinds 9.9.13-(E)-6.11.2024 ]

Translation in E N G L I S H

See above

Oplossing - Solution

$\sqrt{\frac{2+\sqrt 2}{2-\sqrt 2}}=\sqrt{\frac{(2+\sqrt2)(2+\sqrt2)}{(2-\sqrt2)(2+\sqrt2)}}=\sqrt{\frac{(2+\sqrt2)^2}{2^2-(\sqrt2)^2}}=\frac{2+\sqrt2}{\sqrt{4-2}}\\=\frac{(2+\sqrt2)\sqrt2}{\sqrt2\sqrt2}=\frac{2\sqrt2+2}{2}=\sqrt2+1$