Respuesta :

sunflowerem

[tex] \frac{\sqrt{7}-5}{\sqrt{7}+\sqrt{8}} [/tex]

Rationalize.

[tex] -7+2\sqrt{14}+5\sqrt{7}-10\sqrt{2} [/tex]

This can be further simplified to the decimal:

-0.43006...

I hope this helps :)

[tex] \dfrac{\sqrt{7} - 5}{\sqrt{7}+ \sqrt{7} } [/tex]


Rationalise the denominator:


[tex] \dfrac{(\sqrt{7} - 5)(\sqrt{7} - \sqrt{8}) }{(\sqrt{7}+ \sqrt{8}) (\sqrt{7} - \sqrt{8}) }[/tex]


[tex] = \dfrac{(\sqrt{7})^2 - 5\sqrt{7} + 5\sqrt{8}- \sqrt{7}\sqrt{8} }{7 - 8 }[/tex]



[tex] = \dfrac{(7 - 5\sqrt{7} + 10\sqrt{2}- 2\sqrt{14}}{-1 } [/tex]


[tex] = -7 + 5\sqrt{7} - 10\sqrt{2} + 2\sqrt{14} [/tex]


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