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

Video Solution

Solution Steps

00:00 Simplify the following problem

00:03 When there's a root of multiplied terms (A times B)

00:06 We can break it down to the root (A) multiplied by the root (B)

00:09 Apply this formula to our exercise

00:20 Break down 36 to 6 squared

00:25 Break down X to the 4th power to X squared squared

00:31 The root of any number (A) squared cancels out the square

00:35 Apply this formula to our exercise and cancel out the squares

00:51 Break down X squared to X times X

01:00 Simplify wherever possible

01:02 This is 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.