#### Show that \frac{\sqrt{75}-\sqrt{27}}{\sqrt{3}} is an integer and find its value

Anonymous

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Ramanath Parimi

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Identify the prime factors of the radicand inside every radical

Determine the index of the radical

According to the index of the radicals move each group of numbers and variables from inside of the radical to the outside of the radical. If there are not enough numbers or variables to make a group, then leave the numbers inside the radical

Combine the like terms and simplify the expressions both inside and outside of the radical

Check the result obtained satisfies the result type in the question.