Question

Find cube root of 4.096 by prime factorisation method

Answer 1

Hey
Cube root of 4.096

By prime factorisation

3√4.096 = 3√2x2x2x2x2x2x2x2x2x2x2x2
= 2x2x2x2
= 16
Therefore, 3√4.096 = 16

Answer 2

                             Cube Root

If n is a perfect cube for any integer m i.e., n = m³, then m is called the cube root of n and it is denoted by m = ∛n.

Question : Find cube root of 4.096 by prime factorization method.

$\fbox{ANSWER} \\\\ \implies \sqrt[3]{4.096} = \sqrt[3] {\frac{4096}{1000}} = \frac {\sqrt[3]{4096}}{\sqrt[3]{1000}} \\\\ Factors\ of\ 4096\ is \\\\= \big(2\times2\times2\big)\times\big(2\times2\times2\big)\times\big(2\times2\times2\big)\times\big(2\times2\times2\big) \big[we\ makes\ pair\ of\ three \big] \\\\ \therefore \sqrt[3]{4096} = \sqrt[3]{2\times2\times2\times2} = 16 \\\\ Also, \sqrt[3]{100}=\sqrt[3]{10\times10\times10} = 10 \\\\ So, \frac{\sqrt[3]{4096}}{\sqrt[3]{1000}}}=\frac{16}{10} = 1.6$

$Hence, \sqrt[3]{4.096}=\fbox{1.6 answer}$