Simplify the Square Root: √(x^20/x^24) - Step-by-Step Solution

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 When there is a root of a fraction (A divided by B)

00:06 It can be written as root of the numerator (A) divided by root of the denominator (B)

00:09 Apply this formula to our exercise

00:20 When we have a root of the order (B) on number (X) to the power of (A)

00:24 The result equals the number (X) to the power of (A divided by B)

00:33 The "regular" root is of the order 2

00:37 We will apply this formula to our exercise

00:48 Calculate the power quotients

00:56 Break down X to the power of 12 into factors of X to the power of 10 and X squared

01:05 Reduce wherever possible

01:08 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Let's work through the solution step-by-step:

First, simplify the expression inside the square root. We have:

$\frac{x^{20}}{x^{24}} = x^{20-24} = x^{-4}$

Next, apply the square root to the simplified expression:

$\sqrt{x^{-4}} = \left(x^{-4}\right)^{1/2} = x^{-4 \times \frac{1}{2}} = x^{-2}$

This can be written as:

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

Therefore, the solution to the problem is $\frac{1}{x^2}$ .