Question

The cube root of 10648 using prime factorization.​

Answer 1

$\large\bf{\underline{\underline{Answer:}}}$

$\underline{\boxed{\sf\purple{22}}}$

$\large\bf{\underline{\underline{Given :}}}$

$\underline{\boxed{\sf\purple{Number\: =\: 10648}}}$

$\large\bf{\underline{\underline{To\: Find :}}}$

Use prime factorization method to find cube root of $\sf\color{orchid}{10648}$

$\large\bf{\underline{\underline{Solution:}}}$

$\underline{\boxed{\sf\purple{Prime\: Factorization}}}$

2 | 10648

2 | 5324

2 | 2662

11 | 1331

11 | 121

11 | 11

| 1

$\huge{So,}$

$10648 =2 \times 2 \times 2 \times 11 \times 11 \times 11$

$10648 =2^3 \times 11^3$

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

$\sqrt[3]{10648} =2 \times 11$

$\sqrt[3]{10648}$

$\huge{Hence}$

$\large\textbf\color{orange}{cube root of 10648 is 22.}$

Thankyou :)