Solve the Square Root Expression: Simplifying √(25x^4)

Question

Solve the following exercise:

$\sqrt{25x^4}=$

00:00 Simplify the following expression

00:03 The square root of a number (M) multiplied by the square root of another number (N)

00:07 Equals the square root of their product (M times N)

00:14 Apply this formula to our exercise, and convert from root 1 to two

00:20 Break down 25 to 5 squared

00:24 Break down X to the fourth power into X squared squared

00:30 The square root of any number(M) squared cancels out the square

00:37 Apply this formula to our exercise

00:40 This is the solution

To solve the expression $\sqrt{25x^4}$ , we will use the product property of square roots.

First, separate the expression inside the square root into two parts:
$\sqrt{25x^4} = \sqrt{25} \cdot \sqrt{x^4}$ .

Next, simplify each square root:

$\sqrt{25} = 5$ because $5^2 = 25$ .
$\sqrt{x^4} = x^{4/2} = x^2$ since the square root of $x^n$ is $x^{n/2}$ for even $n$ .

Now combine the simplified terms:
$5 \cdot x^2$ .

Therefore, the simplified expression is $5x^2$ .

The correct answer is therefore $\mathbf{5x^2}$ , which corresponds to choice $2$ .

$5x^2$