Question

find the cube root of 46656 by prime factorization method

Answer 1

prime factors of 46656 is 2*2*2*2*2*2*3*3*3*3*3*3"
cube root 2*2*3*3= 36

Answer 2

Cube root of 46656 is 36.

Given:

• 46656

To find:

• Find the cube root using prime factorization.

Solution:

Concept to be used:

$\bf \sqrt[n]{ {a}^{n} } = a$

Step 1:

Find prime factors.

$46656 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$

or

$46656 = {2}^{3} \times {2}^{3} \times {3}^{3} \times {3}^{3}$

Step 2:

Find the cube root of number.

$\sqrt[3]{46656} = \sqrt[3]{ {2}^{3} \times {2}^{3} \times {3}^{3} \times {3}^{3}}$

or

$\sqrt[3]{46656} = \sqrt[3]{(2 \times 2 \times 3 \times 3) ^{3} }$

or

$\sqrt[3]{46656} = \sqrt[3]{(36) ^{3} }$

or

$\bf \sqrt[3]{46656} = 36$

Thus,

Cube root of 46656 is 36.

Learn more:

1) find square root of 1024 by prime factorization method

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2) square of 657666025 by prime factorisation method

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