The correct option is B √(3) =3+√(6)√(75) √(48) √(32)+√(50) =3+√(6)5√(3) 4√(3) 4√(2)+5√(2) =3+√(6)√(3)+√(2)×√(3) √(2)/√(3) √(2) =(3+√( ...

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Simplest Form of a Surd

3+√6√75-√48-√...

Question

$\frac{3 + \sqrt{6}}{\sqrt{75} - \sqrt{48} - \sqrt{32} + \sqrt{50}} =$

\sqrt{2}

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\sqrt{3}

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\sqrt{3} + \sqrt{2}

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\sqrt{3} - \sqrt{2}

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Solution

The correct option is B $\sqrt{3}$
$= \frac{3 + \sqrt{6}}{\sqrt{75} - \sqrt{48} - \sqrt{32} + \sqrt{50}}$
$= \frac{3 + \sqrt{6}}{5 \sqrt{3} - 4 \sqrt{3} - 4 \sqrt{2} + 5 \sqrt{2}}$
$= \frac{3 + \sqrt{6}}{\sqrt{3} + \sqrt{2}} \times \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$
$= (3 + \sqrt{6}) (\sqrt{3} - \sqrt{2})$
$= 3 \sqrt{3} - 3 \sqrt{2} + \sqrt{18} - \sqrt{12}$
$= 3 \sqrt{3} - 3 \sqrt{2} + 3 \sqrt{2} - 2 \sqrt{3}$

$= \sqrt{3}$

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Similar questions

\frac{3 + \sqrt{6}}{\sqrt{75} - \sqrt{48} - \sqrt{32} + \sqrt{50}} =

\frac{3 + \sqrt{6}}{17 \sqrt{3} - 2 \sqrt{32} + 3 \sqrt{18} - 4 \sqrt{48}}

\frac{3 + \sqrt{6}}{17 \sqrt{3} - 2 \sqrt{32} + 3 \sqrt{18} - 4 \sqrt{48}}

\frac{3 + \sqrt{6}}{5 \sqrt{3} - 2 \sqrt{12} - \sqrt{32} + \sqrt{50}}

Find the value of given expression

3 $\sqrt[3]{48}$ -2 $\sqrt[2]{108}$ + 2 $\sqrt[2]{75}$

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