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Write a form of 1 that you can use to rationalize the denominator of the expression  $\frac{10}{\sqrt{3}}$10√3​​ .

Question

Write a form of 1 that you can use to rationalize the denominator of the expression 103\frac{10}{\sqrt{3}}.

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Solution

To rationalize the denominator of the expression 103\frac{10}{\sqrt{3}}, we need to multiply both the numerator and the denominator by the conjugate of the denominator.

The conjugate of 3\sqrt{3} is also 3\sqrt{3}, because the conjugate of a single term is just itself.

So, we multiply both the numerator and the denominator by 3\sqrt{3} to get:

103\frac{10}{\sqrt{3}} * 33\frac{\sqrt{3}}{\sqrt{3}} = 1033\frac{10\sqrt{3}}{3}

So, the form of 1 that we can use to rationalize the denominator of the expression 103\frac{10}{\sqrt{3}} is 33\frac{\sqrt{3}}{\sqrt{3}}.

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