Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\sqrt{1-\frac 14}\cdot \sqrt{1-\frac 19}\cdot \sqrt{1-\frac 1{16}}$ is gelijk aan	A. \(\frac {\sqrt {10}} {4} \)
B. \(\frac {\sqrt 2} {2} \)
C. \(\sqrt 3 \)
D. \(\frac {3} {4} \)
E. \(\frac {\sqrt 5} {4} \)
F. \(\frac {3 \sqrt 2} {4} \)

$\sqrt{1-\frac 14}\cdot \sqrt{1-\frac 19}\cdot \sqrt{1-\frac 1{16}}$ is equal to	A. $\frac {\sqrt {10}} {4} $
	B. $\frac {\sqrt 2} {2} $
	C. $\sqrt 3 $
	D. $\frac {3} {4} $
	E. $\frac {\sqrt 5} {4} $
	F. $\frac {3 \sqrt 2} {4} $

1^ste manier :
$\\\sqrt{1-\frac14}.\sqrt{1-\frac19}.\sqrt{1-\frac1{16}}=\sqrt{\frac{3}{4}}.\sqrt{\frac{8}{9}}.\sqrt{\frac{15}{16}}=\sqrt{\frac{3.8.15}{4.9.16}}=\sqrt{\frac{15}{4.3.2}}=\sqrt\frac58\\=\sqrt{\frac{10}{16}}=\frac{\sqrt{10}}{4}$
2^de manier :
$\\\sqrt{1-\frac14}.\sqrt{1-\frac19}.\sqrt{1-\frac1{16}}=\sqrt{\left(1-\frac12\right)\left(1+\frac12\right)\left(1-\frac13\right)\left(1+\frac13\right)\left(1-\frac14\right)\left(1+\frac14\right)}\\=\sqrt{\frac12.\frac32.\frac23.\frac43.\frac34.\frac54}=\sqrt{\frac{10}{16}}=\frac{\sqrt{10}}{4}$
$\\\sqrt{1-\frac14}.\sqrt{1-\frac19}.\sqrt{1-\frac1{16}}=\sqrt{\left(1-\frac12\right)\left(1+\frac12\right)\left(1-\frac13\right)\left(1+\frac13\right)\left(1-\frac14\right)\left(1+\frac14\right)}\\=\sqrt{\frac12.\frac32.\frac23.\frac43.\frac34.\frac54}=\sqrt{\frac{10}{16}}=\frac{\sqrt{10}}{4}$