Question

Find the value of a ???



$\sqrt{13 - a \sqrt{10} } = \sqrt{8} + \sqrt{5}$
solve it with proper steps.

Answer 1

I just missed to write squaring both sides
that's the answer for your question

Answer 2

hey Amrit ,,,,

√13 - a√10 = √8 + √5
First try and reduce the available roots to forms that are similar to eachother
√10 can be written as √5 × √2  
√8 can be written as 2√2

Now the equation becomes,

√13 - a√5 √2 = 2√2+√5
Thus,
a√5√2 + √5 = √13 - 2√2

√5 (a√2 + 1) = √13 - 2√2

a√2 + 1 = (√13 - 2√2) ÷ √5

a√2  = ( (√13 - 2√2) ÷ √5 ) - 1

Taking L.C.M, 

a√2 =  (√13 - 2√2 - √5) ÷ √5

Thus a= ( √13 / ( √2 √5 ) ) - ( 2 / √5 ) - ( 1 / √2 )

 a= ( √13 / ( √10 ) ) - ( 2 / √5 ) - ( 1 / √2 )

hope it helps u !!!

☺☺ himanshu jha ☺☺