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Question 235645: How would you rationalize the denominator of this expression: square root of x divided by square root of 8y
Answer by MathPro(14)   (Show Source):
You can put this solution on YOUR website! Good Afternoon,
Your problem is:
How would you rationalize the denominator of this expression: square root of x divided by square root of 8y
I’ll write that down using the following notation:
Square root x = sqrt(x) so your problem looks like:
sqrt(x) / sqrt(8y)
This problem can be solved a lot easier if we factor the denominator first:
The number 8 can be rewritten as 2 (2)(2) so we have 2 squared times 2 Lets rewrite the problem now as
sqrt(x)/ sqrt[(2(2)(2)y]=
sqrt(x)/[sqrt[2(2)] sqrt(2y)]
note that sqrt[2(2)] = 2 so we can rewrite the problem as
sqrt(x) / [2sqrt(2y)]
We want to get rid of the square root on the bottom to rationalize it. The product rule states that:
sqrt(x) sqrt(x) = x ^ (1/2 + 1/2) = x^1 = x, where ^ means raise to the power
To apply the product rule to our problem multiply the bottom and top by sqrt(2y) to get:
[ sqrt(2y)sqrt( x)] / [2 sqrt(2y)sqrt(2y)] =
sqrt(2yx) / [2 (2y)] =
sqrt(2yx) / (4y)
Good Luck!
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