Simplify the radical expression by rationalizing the denominator.

8(radicand)48/(radicand) 112x

Please explain how to work this.

If you mean 8√48 / √112x

√48 = √(16*3) = √16 √3 = 4√3
√112 = √(16*7) = √16 √7 = 4√7

8√48/√112x = 8*4√3/4√7x = 8√3/√7x

To rationalize the denominator, multiply by √7/√7 to get

8√21 / 7x

Steve, thank you so much. You are always so helpful.

To simplify the given radical expression and rationalize the denominator, we need to eliminate any radicals from the denominator by multiplying the numerator and the denominator by an expression that will get rid of the radical. Let's break down the steps:

The given radical expression is:

8√48 / √(112x)

First, we need to simplify the radicand in both the numerator and denominator.

√48 = √(16 × 3) = √16 × √3 = 4√3

√(112x) = √(16 × 7 × x) = √16 × √7 × √x = 4√7√x

Now, substitute the simplified values back into the expression:

8(4√3) / 4√7√x

Next, multiply the numerator and denominator by a factor that eliminates the radical from the denominator. In this case, we'll multiply by the conjugate of the denominator:

(8√3) / 4√7√x × (√7√x) / (√7√x)

Now, apply the distributive property to both the numerator and the denominator:

(8√3)(√7√x) / (4√7√x)(√7√x)

Simplify both the numerator and denominator:

(8√21√x) / (4 × 7 × x) = (8√21√x) / (28x)

Now, simplify further by dividing both the numerator and denominator by their greatest common factor (GCF), which is 4:

(2√21√x) / (7x)

Therefore, the simplified radical expression by rationalizing the denominator is:

(2√21√x) / (7x)