Question

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

Answer 1

= 4√X^3

Explanation:

√X x 4√X

X1/2 x X1/4

X1/2 + 1/4

X2+1/4

X3/4

simplify X3/4

= 4√X^3

Answer 2

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

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}`