Question

rationalize the denominator of the following : 1/√5-√2

Answer 1

Answer:

(√5 + √2)/3

Step-by-step explanation:

We have to rationalize :

1/√5 - √2

So, multiply and divide by √5 + √2

∴ (1 )* (√5 + √2)/ (√5 - √2)*(√5 + √2)

{using identity: (a+b)(a-b) = a² - b²}

{So, (√5 - √2)*(√5 + √2) =  (√5)² - (√2)² = 5 - 2 = 3}

So, we can write expression as

(√5 + √2)/3

Now, the denominator is rationalize!

Hope, you got it :-))

Please mark it as brainiest!!

Answer 2

Hope this helps you ;)

$\frac{1}{ \sqrt{5} - \sqrt{2} }$

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

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

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

$= \frac{ \sqrt{5} + \sqrt{2} }{3}$