Simplify the Square Root: √(100x⁴/25x²) Step-by-Step Solution

Video Solution

Solution Steps

00:00 Simplify the following problem

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

00:06 We can break it down to root(A²²²) X root(B)

00:09 We'll apply this formula to our exercise

00:24 Break down 100 into 10 squared

00:27 Break down X⁴ into (X²)²

00:34 reak down 25 into 5 squared

00:38 The root of any number (A) squared cancels out the square

00:42 Apply this formula to our exercise and cancel out the squares:

01:02 Break down X squared into factors X and X

01:09 Simplify wherever possible

01:14 This is the solution

Step-by-Step Solution

Let's solve the problem by following these steps:

Step 1: Simplify the fraction under the square root.
The expression is $\frac{100x^4}{25x^2}$ . We can simplify this by dealing with the coefficient and the variable separately:

The numerical part: $\frac{100}{25} = 4$ .
The variable part: $\frac{x^4}{x^2} = x^{4-2} = x^2$ , using the laws of exponents.

Thus, the simplified fraction is $4x^2$ .

Step 2: Apply the square root.
We have $\sqrt{4x^2}$ . We apply the square root to both terms:

$\sqrt{4} = 2$ , since 2 squared equals 4.
$\sqrt{x^2} = x$ , assuming $x$ is positive (or using the absolute value to ensure non-negativity, but the context suggests a straightforward approach).

Thus, $\sqrt{4x^2} = 2x$ .

Therefore, the solution to the expression is $2x$ .