Simplify Square Root Expression: √(144x^8/16x^2)

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 We can write it as the root of the numerator (A) divided by root of the denominator (B)

00:09 Apply this formula to our exercise

00:22 When we have a root of a multiplication (A times B)

00:26 We can divide it into the root of (A) multiplied by the root of (B)

00:29 Apply this formula to our exercise

00:41 Factorize 144 to 12 squared

00:47 Factorize X to the 8th power to X to the 4th power squared

00:50 Factorize 16 to 4 squared

01:02 The root of any number (A) squared cancels out the square

01:05 Apply this formula to our exercise, and cancel out the squares

01:28 Factorize 12 into factors of 3 and 4

01:33 Factorize X to the 4th power into factors X cubed and X

01:39 Simplify wherever possible

01:48 This is the solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

Now, let’s work through each step:

Step 1: Simplify the fraction $\frac{144x^8}{16x^2}$ .

Divide the coefficients: $\frac{144}{16} = 9$ .

Subtract the exponents of $x$ : $x^{8-2} = x^6$ .

Thus, the simplified fraction is $9x^6$ .

Step 2: Apply the square root property on $9x^6$ .

The square root of a product is the product of the square roots, so we have:

$\sqrt{9x^6} = \sqrt{9} \cdot \sqrt{x^6}$ .

Step 3: Simplify the result.

$\sqrt{9} = 3$ .

$\sqrt{x^6} = x^{\frac{6}{2}} = x^3$ .

Therefore, the expression simplifies to $3x^3$ .

Thus, the solution to the problem is $3x^3$ .