Question

Find the cube root of the result obtained when you subtract $x^3$ from $4097x^3$.​

• A. $16x^3$
• B. $4096x$
• C. $13x^2$
• D. $16x$

Answer 1

The correct option is D

$16x$

According to the question, we want the cube root of the difference between $x^3\text{and}4097x^3$.

Difference = $4097x^3-x^3$
= $4096x^3$

Prime factorization of $4096x^3$
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x $x$ x $x$ x $x$
= $2^4\times 2^4\times 2^4\times x\times x\times x$
= $16\times 16\times 16\times x\times x\times x$
= ${16}^3\times x^3$

You get $\sqrt[3]{34096x^3}$ = $\sqrt[3]{3{16}^3\times x^3}$ = $16x$
So, the cube root of $4096x^3$ is $16x$.