Question

What is the $4^{\text{th}}$ root of 256?

• A. 4
• B. 8
• C. 16
• D. 2

Answer 1

The correct option is A 4

The $4^{\text{th}}$ root of 256 can be written as ${256}^{\frac{1}{4}}.$

We know that $256=4\times 4\times 4\times 4.$

$⟹{256}^{\frac{1}{4}}=(4\times 4\times 4\times 4{)}^{\frac{1}{4}}$

i.e., ${256}^{\frac{1}{4}}=(4^4{)}^{\frac{1}{4}}$

${256}^{\frac{1}{4}}=4^{4\times \frac{1}{4}}(\because (a^m{)}^n=a^{mn})$

${256}^{\frac{1}{4}}=4$

$\therefore$ The $4^{\text{th}}$ root of 256 is 4.