Question

36) Find cube root of 10648 by prime factorization method.​

Answer 1

Here's the required answer to your question

Answer 2

Answer:-

The cube root of 10648 is 22

Solution:-

Prime factorization of 10648:-

$\begin{array}{c | c} 2 & 10648 \\\cline{1-2} 2&5324\\\cline{1-2}2&2662\\\cline{1-2}11&1331\\\cline{1-2}11&121\\\cline{1-2}11&11\\\cline{1-2} &1\end{array}$

By prime factorization we got,

10648 = 2 × 2 × 2 × 11 × 11 × 11

= 2 × 11

= 22

Therefore,

${}^{3} \sqrt{(10648)} = 22$

Now, Verification:-

( 22 )³ = 22 × 22 × 22

( 22 )³ = 10648

Required Answer:-

• The cube root of 10648 is 22.

More Info:-

• A natural number is called a perfect square if, it is the square of some natural number.
• The square of a number is that number raised to the power 2.
• The cube root of a number " x " is the number whose cube is " x ".