The correct option is D √(5) 5+√(10)/5√(5) 2√(20) √(32)+√(50)=5+√(10)/5√(5) 4√(5) 4√(2)+5√(2)=5+√(10)/5√(5) 4√(5) 4√(2)+5√(2) 5+√(10)/√(5)+√(2)×(√(5) √(2)/√(5) ...

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Byju's Answer

Standard X

Mathematics

Addition of Rational Expressions

5+√10/5 √5-2√...

Question

$\frac{5 + \sqrt{10}}{5 \sqrt{5} - 2 \sqrt{20} - \sqrt{32} + \sqrt{50}}$

$5$

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$5 \sqrt{2}$

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$5 \sqrt{5}$

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$\sqrt{5}$

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Solution

The correct option is D
$\sqrt{5}$

$\frac{5 + \sqrt{10}}{5 \sqrt{5} - 2 \sqrt{20} - \sqrt{32} + \sqrt{50}} = \frac{5 + \sqrt{10}}{5 \sqrt{5} - 4 \sqrt{5} - 4 \sqrt{2} + 5 \sqrt{2}} = \frac{5 + \sqrt{10}}{5 \sqrt{5} - 4 \sqrt{5} - 4 \sqrt{2} + 5 \sqrt{2}}$
$\frac{5 + \sqrt{10}}{\sqrt{5} + \sqrt{2}} \times (\frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} + \sqrt{2}}) = \frac{5 \sqrt{5} - 5 \sqrt{2} + \sqrt{50} - \sqrt{20}}{5 - 2} = \frac{3 \sqrt{5}}{3} = \sqrt{5}$

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(32)^{20} \div (32)^{5} = ?

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5+√105√5−2√20−√32+√50

The correct option is D √5 5+√105√5−2√20−√32+√50=5+√105√5−4√5−4√2+5√2=5+√105√5−4√5−4√2+5√2 5+√10√5+√2×(√5−√2√5+√2)=5√5−5√2+√50−√205−2=3√53=√5

$\frac{5 + \sqrt{10}}{5 \sqrt{5} - 2 \sqrt{20} - \sqrt{32} + \sqrt{50}}$