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How to rationalize the denominator

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Instructions and help about rationalize a denominator

here we're asked to rationalize the denominator let's begin by applying the quotient rule for radicals and write this as the square root of 9x divided by the square root of 2y now to rationalize the denominator means to rewrite the fraction without a radical in the denominator so in this case we'll multiply by 1 in the form of the square root of 2y divided by the square root of 2y in this case you could see in the numerator we'll be left with 18 xy or the square root of 18xy divided by the square root of 4y squared now you can see here in the denominator we have the square root of a perfect square if y is considered to be positive the square root of 4y squared will be 2y and in the numerator here we can simplify a little bit let's write 18 as 9 times 2xy and so our final result will be 3 times the square root of 2xy divided by 2y

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