1. simplify the rational expression by rationalizing the denominator?
4 over sqrt 150
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sqrt 189x
(4/√50)/√(189x) * √(189x)/√(189x)
= (4√50 √189x)/(189x)
= 4√(50*189x)/(189x)
= 4√(25*2*9*21x)/(189x)
= 4*5*3√(2*21x)/(189x)
= (20√(42x))/63x
Somehow I suspect a typo
To simplify the rational expression by rationalizing the denominator, we need to get rid of the square root in the denominator.
Let's simplify step by step:
Step 1: Simplify the numerator and denominator individually.
The numerator is 4, which is already simplified.
The denominator is √189x.
Step 2: Simplify the square root in the denominator.
First, let's factor 189.
189 = 9 * 21
Both 9 and 21 are perfect squares, so we can rewrite √189 as √(9 * 21) = √9 * √21 = 3 * √21.
Therefore, the denominator becomes 3 * √21 * x.
Step 3: Rewrite the rational expression with the simplified denominator.
The rational expression becomes:
4 / (3 * √21 * x)
So, the simplified rational expression by rationalizing the denominator is 4 / (3 * √21 * x).
To simplify the rational expression by rationalizing the denominator, we need to get rid of any square roots in the denominator.
In this case, the denominator is √(189x). To rationalize it, we multiply both the numerator and denominator by a factor that eliminates the square root. In this case, we can multiply by √(189x) to eliminate the square root:
4/√(150) * √(189x)/√(189x)
Multiplying the numerators and denominators together:
(4 * √(189x)) / (√(150) * √(189x))
Simplifying further:
(4√(189x)) / √(150 * 189x)
Next, we can simplify the expression inside the square root:
(4√(189x)) / √(28350x)
Taking the square root of 28350x gives:
(4√(189x)) / √(450 * 63x)
Simplifying it further to:
(4√(189x)) / (√450 * √(63x))
Finally, simplifying the square roots gives:
(4√(189x)) / (√450 * 3√(7x))
Therefore, the simplified rational expression by rationalizing the denominator is:
(4√(189x)) / (√450 * 3√(7x))