Simplify sqrt(36x⁴)/sqrt(x²): Square Root Fraction Problem

Video Solution

Solution Steps

00:09 Let's simplify this problem together.

00:12 When taking the square root of multiplied terms, like A times B,

00:17 we can find the root of A, then multiply it by the root of B.

00:22 Now, let's apply this to our exercise.

00:29 We can rewrite 36 as 6 squared.

00:34 And X to the 4th power as X squared, squared.

00:40 Remember, the root of A squared removes the square.

00:45 Let's apply this and remove the squares in our problem.

01:00 Rewrite X squared as X times X.

01:09 Simplify wherever you can.

01:12 And there you have it! That's the solution.

Step-by-Step Solution

To solve the problem, we will simplify the expression step-by-step:

Step 1: Simplify $\sqrt{36x^4}$
We know that $\sqrt{36x^4}$ can be rewritten as $\sqrt{36} \cdot \sqrt{x^4}$ .
First, simplify $\sqrt{36}$ :
$\sqrt{36} = 6$ because $6^2 = 36$ .
Next, simplify $\sqrt{x^4}$ :
$\sqrt{x^4} = x^2$ because $(x^2)^2 = x^4$ .
Step 2: Simplify $\sqrt{x^2}$
$\sqrt{x^2} = x$ (assuming $x \geq 0$ to avoid absolute values).
Step 3: Simplify the expression $\frac{\sqrt{36x^4}}{\sqrt{x^2}}$
Substitute the values obtained in the above steps:
$\frac{\sqrt{36x^4}}{\sqrt{x^2}} = \frac{6x^2}{x}$ .
The expression simplifies to $6x$ as $\frac{x^2}{x} = x$ .

Therefore, the solution to the problem is $6x$ , which matches choice 4.