Show that -125- 64-125-64

⇒√(125× 64)=√(125)×√(64) ⇒√((5)^3× (4)^3)=√((5)^3)×√((4)^3) ⇒ 5× 4=5× 4 ⇒ 20=20 ⇒ 20 20=0 ...

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Standard XII

Mathematics

Binomial Expression

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Question

Show that $\sqrt[3]{125 \times 64} = \sqrt[3]{125} \times \sqrt[3]{64}$

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Solution

$\Rightarrow \sqrt[3]{125 \times 64} = \sqrt[3]{125} \times \sqrt[3]{64}$
$\Rightarrow \sqrt[3]{(5)^{3} \times (4)^{3}} = \sqrt[3]{(5)^{3}} \times \sqrt[3]{(4)^{3}}$
$\Rightarrow 5 \times 4 = 5 \times 4$
$\Rightarrow 20 = 20$
$\Rightarrow 20 - 20 = 0$

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Similar questions

Q. Solve

\sqrt[3]{125 \times 64}

Q. Evaluate

\sqrt[3]{125 \times 64}

Evaluate: ${(\begin{matrix} \frac{64}{125} \end{matrix})}^{\frac{- 2}{3}} \div \frac{1}{(\frac{256}{625})^{\frac{1}{4}}} + (\begin{matrix} \frac{(\sqrt{25})}{\sqrt[3]{64}} \end{matrix})$

Q. Evaluate;

\frac{^{3} \sqrt{- 125 \times 343}}{^{3} \sqrt{(- 27)} \times (- 64)}

Q. Simplify

{(\frac{64}{125})}^{\frac{- 2}{3}}

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Show that 3√125×64=3√125×3√64

⇒3√125×64=3√125×3√64⇒3√(5)3×(4)3=3√(5)3×3√(4)3⇒5×4=5×4⇒20=20⇒20−20=0

Show that $\sqrt[3]{125 \times 64} = \sqrt[3]{125} \times \sqrt[3]{64}$

$\Rightarrow \sqrt[3]{125 \times 64} = \sqrt[3]{125} \times \sqrt[3]{64}$
$\Rightarrow \sqrt[3]{(5)^{3} \times (4)^{3}} = \sqrt[3]{(5)^{3}} \times \sqrt[3]{(4)^{3}}$
$\Rightarrow 5 \times 4 = 5 \times 4$
$\Rightarrow 20 = 20$
$\Rightarrow 20 - 20 = 0$