Solve the Square Root Expression: Simplifying √(196x²/49)

Video Solution

Solution Steps

00:09 Let's simplify this problem step by step.

00:13 When you have the square root of a fraction, like A divided by B, think of it as two separate roots.

00:20 It's the square root of A, divided by the square root of B.

00:24 Now, we will use this approach in our exercise.

00:28 First, break down the number one ninety-six into fourteen squared.

00:35 Next, break down forty-nine into seven squared.

00:42 Remember, the square root of any number, like A squared, removes the square.

00:48 Apply this to our exercise and cancel out the squares. You'll see it gets simpler!

00:58 And there you go, that's how we solve this problem!

Step-by-Step Solution

To solve this problem, we'll apply these steps:

Now, let's perform each step:

Step 1: Simplify the fraction inside the square root:

$\frac{196x^2}{49} = \frac{196}{49} \times x^2$

Simplify $\frac{196}{49}$ : Since $196 \div 49 = 4$ , we have $\frac{196}{49} = 4$ .

The expression therefore simplifies to $4x^2$ .

Step 2: Apply the square root quotient property:

$\sqrt{4x^2} = \sqrt{4} \times \sqrt{x^2}$

Step 3: Simplify each term:

$\sqrt{4} = 2$ and $\sqrt{x^2} = x$ (assuming $x \geq 0$ ).

Therefore, the expression simplifies to $2x$ .

Thus, the solution to the problem is $\boxed{2x}$ .