How can you write the expression with a rationalized denominator?
^3 sqrt 3 / ^3 sqrt 4
To the third power is what that means!
To rationalize the denominator of the expression ^3√3 / ^3√4, follow these steps:
Step 1: Express the denominator in its simplest radical form.
The cube root of 4 can be simplified as follows:
^3√4 = ^3√(2^2) = 2 ^3√1 = 2
Step 2: Rewrite the expression with the simplified denominator.
The expression becomes ^3√3 / 2.
Therefore, the expression with a rationalized denominator is ^3√3 / 2.
To rationalize the denominator, we need to eliminate any square roots from the denominator. In this case, we have the expression (^3 sqrt 3) / (^3 sqrt 4).
Let's start by looking at the denominator (^3 sqrt 4). To rationalize it, we need to simplify the square root of 4. The square root of 4 is 2, so we can rewrite the denominator as (^3 sqrt 4) = (^3 * 2) = (^6).
Now we have (^3 sqrt 3) / (^6). To rationalize this expression, we need to get rid of the cube root (^3) in the numerator.
To do this, we can raise both the numerator and denominator to the power of 3, which will cancel out the cube root.
(^3 sqrt 3) / (^6) can be rewritten as (^3 sqrt 3)^3 / (^6)^3 = 3 sqrt 3 / 6.
The expression with a rationalized denominator is 3 sqrt 3 / 6.