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Question
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
Options
−5
−6
−4
−2
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Solution
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`.
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