Question

How can i find the cube root of 10648 by prime factorization

Answer 1

$\bold {\huge {Solutions :-}}$


Find the cube root of 10648 by prime factorization :-

By prime factorization. $\bold {We get,}$

10648 = 2 × 2 × 2 × 11 × 11 × 11
= 2³ × 11³


$\bold {\underline {Now,}}$

$\sqrt[3]{10648} = \sqrt{{(2 \times 11) }^{3} } \\ = 2 \times 11 = 22$


$\bold {\underline {Hence, }}$

$\bold {The ~cube ~root ~of ~10648~ is ~22.}$

Answer 2

${\mathcal {\huge {\bold {Hey}}}}$

${\bold{\huge {Solutions :-}}}$

${\underline {\bold {By \: Prime \: Factorisation \: We \: Get}}}$

↪️10648 ➡️ 2 × 2 × 2 × 11 × 11 × 11
➡️ 2 ^ 3 × 11 ^ 3

Now,

$\sqrt[3]{10648} = \sqrt{ {(2 \times 11)}^{3} } \\ = > 2 \times 11 = 22$

$\underline \bold {Hence,}$ the cube root of 10648 = 22