Multiplyi -13-5ii -32-8-

(i) √(13)×√(5)=√(13× 5)=√(65) (ii) √(32)×√(8)=√(32× 8) =√(2^5× 2^3)=√(2^8)=√(2^4× 2^4)=2× 2=4 ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

Multiplyi √...

Question

Multiply
(i) $\sqrt[3]{13} \times \sqrt[3]{5}$
(ii) $\sqrt[4]{32} \times \sqrt[4]{8}$ .

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Solution

(i) $\sqrt[3]{13} \times \sqrt[3]{5} = \sqrt[3]{13 \times 5} = \sqrt[3]{65}$
(ii) $\sqrt[4]{32} \times \sqrt[4]{8} = \sqrt[4]{32 \times 8}$
$= \sqrt[4]{2^{5} \times 2^{3}} = \sqrt[4]{2^{8}} = \sqrt[4]{2^{4} \times 2^{4}} = 2 \times 2 = 4$

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Similar questions

Multiply:
(i) $\sqrt{3} (\sqrt{7} - \sqrt{3})$

(ii) $(\sqrt{5} - \sqrt{7}) \sqrt{2}$

(iii) $(3 \sqrt{2} - \sqrt{3}) (4 \sqrt{3} - \sqrt{2})$

Q. Simplify

(i)

\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}

(ii)

\frac{1}{\sqrt{3} + \sqrt{2}} - \frac{2}{\sqrt{5} - \sqrt{3}} - \frac{3}{\sqrt{2} - \sqrt{5}}

(iii)

\frac{2 + \sqrt{3}}{2 - \sqrt{3}} + \frac{2 - \sqrt{3}}{2 + \sqrt{3}} + \frac{\sqrt{3} - 1}{\sqrt{3} + 1}

(iv)

\frac{2 \sqrt{6}}{\sqrt{2} + \sqrt{3}} + \frac{6 \sqrt{2}}{\sqrt{6} + \sqrt{3}} - \frac{8 \sqrt{3}}{\sqrt{6} + \sqrt{2}}

Q. Simplify
(i)

(10 + \sqrt{3}) (2 + \sqrt{5})

(ii)

(\sqrt{5} + \sqrt{3})^{2}

(iii)

(\sqrt{13} - \sqrt{2}) (\sqrt{13} + \sqrt{12})

(iv)

(8 + \sqrt{3}) (8 - \sqrt{3})

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Find the value of:

(i) $(- 4) \div \frac{2}{3}$

(ii) $\frac{- 3}{5} \div 2$

(iii) $\frac{- 4}{5} \div - 3$

(iv) $\frac{- 1}{8} \div \frac{3}{4}$

(v) $\frac{- 2}{13} \div \frac{1}{7}$

(vi) $\frac{- 7}{12} \div \frac{- 2}{13}$

(vii) $\frac{3}{13} \div \frac{- 4}{65}$

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Multiply(i) 3√13×3√5(ii) 4√32×4√8.

(i) 3√13×3√5=3√13×5=3√65(ii) 4√32×4√8=4√32×8=4√25×23=4√28=4√24×24=2×2=4

Multiply
(i) $\sqrt[3]{13} \times \sqrt[3]{5}$
(ii) $\sqrt[4]{32} \times \sqrt[4]{8}$ .

(i) $\sqrt[3]{13} \times \sqrt[3]{5} = \sqrt[3]{13 \times 5} = \sqrt[3]{65}$
(ii) $\sqrt[4]{32} \times \sqrt[4]{8} = \sqrt[4]{32 \times 8}$
$= \sqrt[4]{2^{5} \times 2^{3}} = \sqrt[4]{2^{8}} = \sqrt[4]{2^{4} \times 2^{4}} = 2 \times 2 = 4$