Question

Combine, and simplify the following radical expressions: √7-5/√7+√8

Answer 1

$\frac{\sqrt{7}-5}{\sqrt{7}+\sqrt{8}}$

Rationalize.

$-7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2}$

This can be further simplified to the decimal:

-0.43006...

I hope this helps :)

Answer 2

$\dfrac{\sqrt{7} - 5}{\sqrt{7}+ \sqrt{7} }$

Rationalise the denominator:

$\dfrac{(\sqrt{7} - 5)(\sqrt{7} - \sqrt{8}) }{(\sqrt{7}+ \sqrt{8}) (\sqrt{7} - \sqrt{8}) }$

$= \dfrac{(\sqrt{7})^2 - 5\sqrt{7} + 5\sqrt{8}- \sqrt{7}\sqrt{8} }{7 - 8 }$

$= \dfrac{(7 - 5\sqrt{7} + 10\sqrt{2}- 2\sqrt{14}}{-1 }$

$= -7 + 5\sqrt{7} - 10\sqrt{2} + 2\sqrt{14}$