express the entire radicals as mixed number

Question

√96x^3

Answer 1

To express √96x^3 as a mixed number, we need to simplify the square root and then express it as a mixed number.

First, we can simplify the square root of 96x^3.

To do this, we break down 96x^3 into its prime factors:
96 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
x^3 = x * x * x

Now, we can simplify the square root using the property √(ab) = √a * √b:
√96x^3 = √(2^4 * 3 * x * x * x) = √(2^4) * √(3) * √(x) * √(x) * √(x) = 2^2 * √(3) * x^1.5

Next, we can simplify 2^2, which equals 4:
4 * √(3) * x^1.5 = 4√(3)x^1.5

So the expression √96x^3 can be simplified to 4√(3)x^1.5.

Answer 2

√96x^3 = √(16x^2 * 6x) = 4x √6x

Answer 3

Apologies for the previous error. You are correct.

To express √96x^3 as a mixed number, we can simplify the expression as follows:

√96x^3 = √(16x^2 * 6x)

Using the property √(ab) = √a * √b, we can express this as:

√96x^3 = √16x^2 * √6x = 4x √6x

So, the entire radicals can be expressed as a mixed number 4x √6x.