How do you figure out simplest radical form with variables and/or exponents and/or numbers outside the square root
if taking nth roots, look for nth powers and take them out of the radical, since the nth-root of x^n = x
example:
√300 = √100√3 = 10√3
∛640 = ∛64∛10 = 4∛10
∜80 = ∜16∜5 = 2∜5
What is the 9th root of 64, in simplest radical form?
To figure out the simplest radical form with variables, exponents, and numbers outside the square root, follow these steps:
Step 1: Simplify any variables or exponents inside the square root. If there are multiple factors inside the square root, simplify them individually. For example, if you have √(x^2), simplify it to x.
Step 2: Simplify any numbers or expressions outside the square root. For example, if you have 2√3, multiply the number outside (√3) with the number inside (√3) to get 2√(3*3) = 2√9. Then simplify 2√9 to 2*3 = 6.
Step 3: Combine the simplified values from steps 1 and 2. This will give you the simplest radical form with variables, exponents, and numbers outside the square root.
Let's take an example to understand the process:
Simplify the expression √(2x^2y^3) * √(3z^2).
Step 1: Simplify variables and exponents inside the square roots:
- √(2x^2y^3) becomes x*y√(2y).
- √(3z^2) becomes z√3.
Step 2: Simplify any numbers or expressions outside the square roots. However, in this example, there are no numbers outside the square root, so we move to the next step.
Step 3: Combine the simplified values from step 1.
- x*y√(2y) * z√3 = xyz√(2y√3).
The expression xyz√(2y√3) is the simplest radical form with variables, exponents, and numbers outside the square root.
Remember to simplify each component individually before combining them.