1. simplify the rational expression by rationalizing the denominator?
4 over sqrt 150
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sqrt 189x
Not sure of your notation.
4/√150 divided by √189x?
To rationalize the denominator of the rational expression, we need to eliminate the square root from the denominator. Here's how you can simplify the expression:
Step 1: Simplify both the numerator and the denominator separately.
Numerator: 4 remains as it is.
Denominator: The square root of 150 can be simplified as follows: √150 = √(25 * 6) = √25 * √6 = 5√6.
So the expression becomes:
4/√150
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√189x = 4/(5√6) / √189x
Step 2: Rationalize the denominator.
To rationalize the denominator, we need to get rid of the square root in the denominator. To do this, we'll multiply both the numerator and denominator by the conjugate of the denominator, which is (√189x).
4/(5√6) / √189x * (√189x)/(√189x) = 4√189x/(5√6 * √189x)
Step 3: Simplify the expression.
Now, simplify the expression further by multiplying the like terms:
4√189x/(5√6 * √189x) = (4/5) * (√189x/√6 * √189x) = (4/5) * (√189x)^2/√6
Simplifying the expression inside (√189x)^2 gives us:
(4/5) * 189x/√6 = (4 * 189x)/(5√6) = (756x)/(5√6)
So, the simplified rational expression after rationalizing the denominator is (756x)/(5√6).