Question

If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]

Options

• −5

• −6

• −4

• −2

Answer 1

Given that:`sqrt(13- a sqrt10)= sqrt8 +sqrt5`

We need to find a

The given expression can be simplified by taking square on both sides 

`(sqrt(13- a sqrt10)^2)= (sqrt8 +sqrt5)^2`

`13-asqrt10 = (sqrt8)^2 +(sqrt5)^2 + 2xx sqrt8xx sqrt5`

                    `= 8+ 5 +2sqrt40`

The irrational terms on right side can be factorized such that it of the same form as left side terms. 

Hence,

`13 - asqrt10 = 13 +2 sqrt4 sqrt10`

` =13+2xx2xxsqrt10`

`= 13+4sqrt10.`

On comparing rational and irrational terms, we get `a=-4`.