Question

Q1 find the cube root by prime factorization-
1. 125000

Answer 1

$\begin{array}{r | l}</p><p></p><p>2 & \underline{1,25,000}</p><p>\end{array}$

$\begin{array}{r | l}</p><p>2 & \underline{62,500}</p><p>\end{array}$

$\begin{array}{r | l}</p><p> 2 & \underline{31,250}</p><p>\end{array}$

$\begin{array}{r | l}</p><p> 5 & \underline{15,625 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p>5 &\underline{ 3,125 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p> 5 & \underline{625 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p>5 & \underline{125 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p> 5 & \underline{25 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p>5 & \underline{5 }</p><p>\end{array}$

$\begin{array}{r | l}</p><p>1 & 1</p><p>\end{array}$

$\sf \implies \sqrt[3]{ \underline{2 \times 2 \times 2} \: \times\underline{ 5 \times 5 \times 5 } \: \times \underline{</p><p>5 \times 5 \times 5}}$

As we take only one term in 3 same terms in prime factorization to find cube root.

$\sf \implies 2 \times 5 \times 5$

$\sf\implies 50$

______________________________

2 |125000

2 |62500

2 |31250

5 |15625

5 |3125

5 |625

5 |125

5 |25

5 |5

| 1

$\sf \implies \sqrt[3]{ \underline{2 \times 2 \times 2} \: \times\underline{ 5 \times 5 \times 5 } \: \times \underline{</p><p>5 \times 5 \times 5}}$

As we take only one term in 3 same terms in prime factorization to find cube root.

$\sf \implies 2 \times 5 \times 5$

$\sf\implies 50$