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The Value of √ 5 + 2 √ 6 is - Mathematics

MCQ

The value of \[\sqrt{5 + 2\sqrt{6}}\] is

Options

  • \[\sqrt{3} - \sqrt{2}\]

  • \[\sqrt{3} + \sqrt{2}\]

  • \[\sqrt{5} + \sqrt{6}\]

  • none of these

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Solution

Given that:`sqrt(5+2sqrt6)`.It can be written in the form   `(a-b )^2 = a^2 +b^2 - 2 ab` as

`sqrt(5+2sqrt6) = sqrt(3+2+2xxsqrt3 xxsqrt2)`

` =sqrt((sqrt3)^2 + (sqrt2)^2+ 2 xx sqrt3 xxsqrt2)`

`= sqrt((sqrt3+sqrt2)^2)`

` = sqrt3 +sqrt2.`

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Q 20 | Page 18
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