Simplify the Square Root Expression: √(64x²/x⁴)

Video Solution

Solution Steps

00:00 Simplify the following problem

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

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

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

00:15 When there's a root of multiplication (A times B)

00:19 It can be divided into root of (A) times root of (B)

00:22 We'll apply this formula to our exercise

00:32 Let's factor 64 into 8 squared

00:38 Let's factor X to the fourth power into X squared squared

00:44 The root of any number (A) squared cancels out the square

00:47 Apply this formula to our exercise, and proceed to cancel out the squares

00:59 Let's factor X squared into factors X and X

01:05 Reduce wherever possible

01:09 This is the solution

Step-by-Step Solution

To solve this problem, we'll simplify the expression inside the square root step-by-step:

Step 1: Simplify the fraction $\frac{64x^2}{x^4}$ using the quotient rule for exponents:

$\sqrt{\frac{64x^2}{x^4}} = \sqrt{64x^{-2}} = \sqrt{64} \cdot \sqrt{x^{-2}}$ .
$\sqrt{64} = 8$ and $\sqrt{x^{-2}} = x^{-1}$ (since it represents inverse squaring).
Thus, $\sqrt{64x^{-2}} = 8 \cdot x^{-1} = \frac{8}{x}$ .

Therefore, the solution to the problem is $\frac{8}{x}$ , which matches choice 1.