entire radicals to mixed radicals
√96x^3
why stop there?
√96x^3 = √(16x^2 * 6x) = 4x√(6x)
You're right, I apologize for stopping prematurely. We can simplify further by taking out any perfect square factors from under the square root.
√(16x^2 * 6x) = √(16x^2) * √(6x) = 4x * √(6x).
So, √96x^3 can be written as 4x * √(6x), which is a simpler mixed radical. Thank you for pointing that out!
To simplify √96x^3 from an entire radical to a mixed radical, you can break down the number under the square root sign into its prime factors and then simplify.
1. Begin by factoring out the perfect square from the number 96 and separate the variable term (x^3):
√(16 * 6 * x^2 * x)
2. Simplify the perfect square, which is 16, by taking its square root:
4 * √(6 * x^2 * x)
3. Rearrange the terms under the square root sign, grouping the terms with the same exponent:
4 * √(6 * x^2 * x)
4. Simplify the square root separately for each term:
4 * ( √6 * √(x^2) * √x )
5. The square root of x^2 equals x, so simplify:
4 * ( √6 * x * √x )
Now, you have the mixed radical form of √96x^3, which is: 4 * √6x * √x
To convert √96x^3 from entire radicals to mixed radicals, we first need to find the largest perfect square factor of 96x^3.
Since 96 is not a perfect square, we can find its prime factorization: 96 = 2^5 * 3^1.
To find the largest perfect square factor of 96x^3, we can look at the exponents of the prime factors. The largest perfect square factor is 2^4 = 16.
We can then write √96x^3 as √(16 * 6 * x^2 * x).
Using the property of radicals, we can split the square root and simplify:
√(16 * 6 * x^2 * x) = √(16) * √(6) * √(x^2) * √(x) = 4√(6x^2) * √(x).
So, √96x^3 can be written as 4√(6x^2) * √(x), which is a mixed radical.