How do I solve for the square root of 15/x^3?
Really nothing to "solve" here, since there is no equation.
You can rewrite it in several ways, here is one way:
√(15/x^3)
= √15/(x√x)
or you could rationalize it
√(15/x^3)
= √(15/x^3) * √x^3/√x^3
= √15 x√x /x^3
= √(15x)/x^2
other variations are also possible
Or well, it says "simplify the radical expression." I know the answer is √15/x but I don't understand how to get it.
√(15/x^3) , (your question ) is not equal to √15/x
e.g. let x = 2
√(15/x^3) = √(15/8) = 1.3693..
√15/x = √15/2 = 1.93649...
test x = 2 in both of my answers, it works
Oops!! I'm so sorry. I just realized that I wrote the problem wrong. It's actually 15x/x^3
Nevermind, I figured out how to do it.
To solve for the square root of 15/x^3, you can follow these steps:
1. Simplify the expression inside the square root, if possible. In this case, the expression is already in its simplest form.
2. Rewrite the square root as a fractional exponent. The square root (√) is the same as raising the expression to the power of 1/2. So, the expression becomes (15/x^3)^(1/2).
3. Apply the exponent to each term inside the parentheses. Raise 15 to the power of 1/2 and x^3 to the power of 1/2. This yields (√15) / (√x^3).
4. Simplify further by using exponent rules. The square root of 15 is an irrational number since it cannot be expressed as a fraction. So, it remains as (√15). For the square root of x^3, you can simplify it as x^(3/2) since the square root of x^3 is equivalent to raising x to the power of 3/2.
Therefore, the final answer is (√15) / (x^(3/2)), where (√15) denotes the square root of 15 and x^(3/2) represents x raised to the power of 3/2.