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Write a form of $1$1​ that you can use to rationalize the denominator of the expression  $\frac{4}{\sqrt{6}}$4√6​​ .

Question

Write a form of 111​ that you can use to rationalize the denominator of the expression  46\frac{4}{\sqrt{6}}4√6​​ .

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Solution

To rationalize the denominator of the expression 46\frac{4}{\sqrt{6}}, we need to multiply both the numerator and the denominator by a form of 1 that will eliminate the square root in the denominator.

The square root of a number can be eliminated by multiplying it by itself. Therefore, we can use 6\sqrt{6} as the form of 1 to rationalize the denominator.

However, we can't just multiply the denominator by 6\sqrt{6}, we also have to multiply the numerator by 6\sqrt{6} to keep the value of the fraction the same. This is because 66\frac{\sqrt{6}}{\sqrt{6}} is equivalent to 1.

So, the form of 1 that we can use to rationalize the denominator of the expression 46\frac{4}{\sqrt{6}} is 66\frac{\sqrt{6}}{\sqrt{6}}.

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