express the entire radicals as mixed number
√96x^3
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.
√96x^3 = √(16x^2 * 6x) = 4x √6x
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.
To express the entire radical √96x^3 as a mixed number, we can simplify the square root and then express it as a mixed number.
First, let's simplify the square root of 96x^3:
√96x^3 = √(16 * 6 * x^2 * x) = √16 * √6 * √x^2 * √x = 4 * √6 * x * √x = 4x√(6x).
Now that we have simplified the radical, we can express it as a mixed number:
To convert 4x√(6x) into a mixed number, we need to determine the whole number and the fractional part.
The whole number part can be obtained by dividing the coefficient of the radical (4x) by the square root of the number under the radical (√(6x)).
whole number part = coefficient of the radical / square root of the number under the radical
whole number part = 4x / (√(6x)).
To express the fractional part, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.
fractional part = (coefficient of the radical * conjugate of the denominator) / (square root of the number under the radical * conjugate of the denominator).
fractional part = (4x * (√(6x))) / ((√(6x)) * (√(6x))).
fractional part = (4x * (√(6x))) / (6x).
Simplifying the fractional part gives us:
fractional part = (4x * (√(6x))) / (6x) = (2√(6x)) / 3.
Therefore, √96x^3 can be expressed as the mixed number:
4x + (2√(6x) / 3).