Question

What is the value of $\sqrt[3]{364}÷\sqrt[3]{3-64}$ ?

• A. $-1$
• B. $0$
• C. $1$
• D. $16$

Answer 1

The correct option is A $-1$

On prime factorising, we get,

$64=\underset{–}{4\times 4\times 4}$ $=4^3$.

Then, $-64$ $=(-4{)}^3$.

Therefore, value of $\sqrt[3]{364}÷\sqrt[3]{3-64}$ is:

$\sqrt[3]{364}÷\sqrt[3]{3-64}$

$=\sqrt[3]{34^3}÷\sqrt[3]{3(-4{)}^3}$

$=4÷(-4)=-1$.

Therefore, option $A$ is correct.