What is the simplest form of the radical expression √2+√5/√2-√5

Asked by maham237 @ 17/12/2020 in Mathematics viewed by 343 People

What is the simplest form of the radical expression? Sqrt 2+ sqrt 5 / sqrt 2 - sqrt 5

Answered by maham237 @ 17/12/2020

Answer:

$-(7+2\sqrt{10})/3$

Step-by-step explanation:

we have

$\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}}$

we know that

We can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator

$\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}-\sqrt{5}} *\frac{\sqrt{2}+\sqrt{5}}{\sqrt{2}+\sqrt{5}}=( \sqrt{2}+\sqrt{5})^{2}/(2-5)\\ \\=(2+2\sqrt{10}+5)/(-3)\\ \\(7+2\sqrt{10})/(-3)\\ \\=-(7+2\sqrt{10})/3$

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