Question

Find the cube root of 9261 using prime factorization method please
Write the steps

Answer 1

Answer:

My question was originally -9621 but I will give you answer in both positive and negative.

Step-by-step explanation:

9621 ÷3=3087

3087÷3=1029

1029÷3=343

343÷7=49

49÷7=7

7÷7=1

Answer 2

The cube root of 9261 = 21

Given :

The number 9261

To find :

The cube root of 9261 using prime factorization method

Solution :

Step 1 of 2 :

Prime factorise the given number

The given number is 9261

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:9261 \:\:}}}\\ {\underline{\sf{3}}}&\underline{\sf{\:\:3087 \:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:1029 \:\:}} \\\underline{\sf{7}}&\underline{\sf{\:\:343\:\:}}\\\underline{\sf{7}}&\underline{\sf{\:\:49\:\:}} \\ {\underline{\sf{7}}}&\underline{\sf{\:\:7\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

Thus on prime factorisation we get

9261 = 3 × 3 × 3 × 7× 7 × 7

∴ 9261 = 3³ × 7³

Step 2 of 2 :

Find the cube root of the number

$\displaystyle \sf{ }\sqrt[3]{9261}$

$\displaystyle \sf{ = }\sqrt[3]{ {3}^{3} \times {7}^{3} }$

$\displaystyle \sf{ } = 3 \times 7$

$\displaystyle \sf{ } = 21$