Question

What is the expression in radical form?

Answer 1

Answer:

The simplest form is 128√2

Step-by-step explanation:

Let the expression be: $8^{\frac{5}{2}}$

We know that a square root can also be written as a power of 1/2:

$\sqrt{x} = x^\frac{1}{2}$

Simplify the given expression:

$8^\frac{5}{2} = 8^{5\cdot\frac{1}{2}}$

write it in the square root form

$8^{5\cdot\frac{1}{2}} = \sqrt{8^5}$

simplify the expression even further

$\sqrt{8^5}= \sqrt{8^2\cdot8^2\cdot8} \\\sqrt{8^2\cdot8^2\cdot8} = \sqrt{8^2}\sqrt{8^2}\sqrt{8}$

where the terms with power 2 cancels the square root.

$\sqrt{8^2} \sqrt{8^2} \sqrt{8} = 8\cdot8\cdot\sqrt{8} =64\sqrt{8}$

Simplify the expression under radical sign

$64\sqrt{8} = 64\sqrt{2\cdot2\cdot2} \\64\sqrt{2\cdot2\cdot2} = 64\sqrt{2^2}\sqrt{2} \\64\sqrt{2^2}\sqrt{2} =64\cdot2\sqrt{2} \\64\cdot2\sqrt{2} =128\sqrt{2}$