Question
entire radicals to mixed radicals
√96x^3
√96x^3
Answers
Answered by
oobleck
why stop there?
√96x^3 = √(16x^2 * 6x) = 4x√(6x)
√96x^3 = √(16x^2 * 6x) = 4x√(6x)
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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!
√(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!