Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De breuk $https://latex.codecogs.com/png.image?\dpi{110}\frac{13.9^{\sqrt 6}+14.3^{\sqrt{24}}}{\left ( 5.3^{\sqrt 6}-2.3^{\sqrt 6} \right )^2 }$ kan vereenvoudigd worden tot	A. 27
	B. 243
	C. 3
	D.
	E. 9

[ 6-5414 - op net sinds 8.10.08-(E)-4.11.2023 ]

Translation in E N G L I S H

The fraction $https://latex.codecogs.com/png.image?\dpi{110}\frac{13.9^{\sqrt 6}+14.3^{\sqrt{24}}}{\left ( 5.3^{\sqrt 6}-2.3^{\sqrt 6} \right )^2 }$ can be simplified to	A. 27
	B. 243
	C. 3
	D.
	E. 9

Oplossing - Solution

$\frac{13.9^{\sqrt 6}+14.3^{\sqrt{24}}}{\left(5.3^{\sqrt 6}-2.3^{\sqrt 6}\right)^2}\overset{\sqrt{24}=\sqrt{4.6}}{=}\frac{13.3^{2.\sqrt 6}+14.3^{2\sqrt{6}}}{\left(3.3^{\sqrt 6}\right)^2}=\frac{27.3^{2.\sqrt6}}{9.3^{2.\sqrt6}}=\frac{27}{9}=3$