Cube root of an integer:Prime factorization of 40 is 40=2× 2× 2× 5Also, the cube root of 40 in exponential form is (40)^1/3 and in radical form is √(40 )or 2 √( ...

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Byju's Answer

Standard VIII

Mathematics

Cube Root Using Prime Factorisation

Simplify √40.

Question

Simplify $\sqrt[3]{40}$ .

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Solution

Cube root of an integer:
Prime factorization of $40$ is
$40 = 2 \times 2 \times 2 \times 5$
Also, the cube root of 40 in exponential form is ${(40)}^{\frac{1}{3}}$ and in radical form is $\sqrt[3]{40} o r 2 \sqrt[3]{5}$ .
Hence, $\sqrt[3]{40}$ is equal to $2 \sqrt[3]{5}$ .

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Simplify 403.

Cube root of an integer:Prime factorization of 40 is 40=2×2×2×5Also, the cube root of 40 in exponential form is (40)13 and in radical form is 403or253.Hence,403 is equal to 253.

Simplify $\sqrt[3]{40}$ .

Cube root of an integer:
Prime factorization of $40$ is
$40 = 2 \times 2 \times 2 \times 5$
Also, the cube root of 40 in exponential form is ${(40)}^{\frac{1}{3}}$ and in radical form is $\sqrt[3]{40} o r 2 \sqrt[3]{5}$ .
Hence, $\sqrt[3]{40}$ is equal to $2 \sqrt[3]{5}$ .