Question

1upon (root5-2). plz solve.

Answer 1

1/√5 -2 =√5 +2 /5-4 =√5 +2 answer

Answer 2

Hi friend, Harish here.

Here is your answer:

Given number:    $\frac{1}{ \sqrt{5} - 2 }$

Now we must rationalize the denominator of the given number.

To rationalize the number we must multiply and divide it by it's conjugate.

Conjugate of denominator is √5 + 2.

Then,

⇒  $\frac{1}{ \sqrt{5} - 2 }\times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{(\sqrt{5} +2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)}$

we know that, (a + b) (a - b) = a² - b²

⇒ (√5 - 2) (√5 + 2) = (√5)² - (2)² = 5 - 4 = 1.

Then,

⇒  $\frac{\sqrt{5} + 2}{(\sqrt{5} - 2)(\sqrt{5} + 2)} = \frac{\sqrt{5} - 2}{1} = \sqrt{5} + 2$

Therefore the answer is √5 + 2.
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Hope my answer is helpful to you.