The correct option is C 30 √(899) √(31) √(29)/√(31)+√(29) Multiply and divide by √(31) √(29) ⇒√(31) √(29)/√(31)+√(29)×√(31) √(29)/√(31) √(2 ...

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Identities for Irrational Numbers

√31-√29/√31+√...

Question

$\frac{\sqrt{31} - \sqrt{29}}{\sqrt{31} + \sqrt{29}}$ equals

60 - 2 \sqrt{899}

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60 \sqrt{899}

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30 - \sqrt{899}

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\frac{1}{30 - \sqrt{899}}

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Solution

The correct option is C $30 - \sqrt{899}$
$\frac{\sqrt{31} - \sqrt{29}}{\sqrt{31} + \sqrt{29}}$
Multiply and divide by $\sqrt{31} - \sqrt{29}$
$\Rightarrow \frac{\sqrt{31} - \sqrt{29}}{\sqrt{31} + \sqrt{29}} \times \frac{\sqrt{31} - \sqrt{29}}{\sqrt{31} - \sqrt{29}}$
$\Rightarrow \frac{31 + 29 - 2 \sqrt{31} \sqrt{29}}{31 - 29}$
$\Rightarrow \frac{60 - 2 \sqrt{899}}{2}$
$\Rightarrow \frac{2 (30 - \sqrt{899})}{2}$
$\Rightarrow 30 - \sqrt{899}$

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