(√(3)+√(2))(√(5)+√(7)) = [(√(3)×√(5))+(√(3)×√(7))] nbsp; [(√(2)×√(5))+(√(2)×√(7))] = (√(15)+√(21))+(√(10)+√(14)) = nbsp; nbsp;√(15)+√(21)+√(10)+√(14) ...

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Byju's Answer

Standard VIII

Mathematics

Finding Square Root through Prime Factorisation

Simplify: √3+...

Question

Simplify: ( $\sqrt{3} + \sqrt{2})$ $(\sqrt{5} + \sqrt{7})$

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Solution

$(\sqrt{3} + \sqrt{2}) (\sqrt{5} + \sqrt{7}) = [(\sqrt{3} \times \sqrt{5}) + (\sqrt{3} \times \sqrt{7})] [(\sqrt{2} \times \sqrt{5}) + (\sqrt{2} \times \sqrt{7})] = (\sqrt{15} + \sqrt{21}) + (\sqrt{10} + \sqrt{14}) = \sqrt{15} + \sqrt{21} + \sqrt{10} + \sqrt{14}$

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Similar questions

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\frac{2}{5} + \frac{3}{7} + (\frac{- 6}{5}) + (\frac{- 13}{7})

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(ii) $\frac{7 + 3 \sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3 \sqrt{5}}{3 - \sqrt{5}}$

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\frac{3^{5} 2^{2} 7^{3}}{7^{2} 3^{3} 2^{4}}

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Q. Simplify :

\frac{7 \sqrt{3}}{\sqrt{10} + \sqrt{3}} - \frac{2 \sqrt{5}}{\sqrt{6} + \sqrt{5}} - \frac{3 \sqrt{2}}{\sqrt{15} + 3 \sqrt{2}}

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Simplify: (√3+√2)(√5+√7)

(√3+√2)(√5+√7)=[(√3×√5)+(√3×√7)][(√2×√5)+(√2×√7)]=(√15+√21)+(√10+√14)=√15+√21+√10+√14

Simplify: ( $\sqrt{3} + \sqrt{2})$ $(\sqrt{5} + \sqrt{7})$

$(\sqrt{3} + \sqrt{2}) (\sqrt{5} + \sqrt{7}) = [(\sqrt{3} \times \sqrt{5}) + (\sqrt{3} \times \sqrt{7})] [(\sqrt{2} \times \sqrt{5}) + (\sqrt{2} \times \sqrt{7})] = (\sqrt{15} + \sqrt{21}) + (\sqrt{10} + \sqrt{14}) = \sqrt{15} + \sqrt{21} + \sqrt{10} + \sqrt{14}$