Question

Rewrite in simplest radical form square root of x times the fourth root of x. Show each step of your process.

Answer 1

Answer:

$\sqrt[4] {x^3}$

Step-by-step explanation:

At this point, we can transform the square root into a fourth root by squaring the argument, and bring into the other root:

$\sqrt x \cdot \sqrt[4] x =\sqrt [4] {x^2} \cdot \sqrt[4] x = \sqrt[4]{x^2\cdot x} = \sqrt[4] {x^3}$

Alternatively, if you're allowed to use rational exponents, we can convert everything:

$\sqrt x \cdot \sqrt[4] x = x^{\frac12} \cdot x^\frac14 = x^{\frac12 +\frac14}= x^{\frac24 +\frac14}= x^\frac34 = \sqrt[4] {x^3}$