Factor any numerical values that are perfect squares, cubes or the product of some other exponential power. For instance, if you have √4 + √9, the square root of 4 is 2 and the square root of 9 is 3. Therefore, the problem can be simplified to 2 + 3, which equals 5.
Add or subtract like terms. For instance, you can add 2√3 + 3√3 to get 5√3. You may have to extract roots before doing this. For example, if the equation was 2√3 + 3√12, you can simplify 3√12 to 3√4*√3. The square root of 4 is 2. Therefore, you would have 3*2√3, which equals 6√3. Insert this back into the equation to get 2√3 + 6√3, which equals 8√3. Follow the same procedures for subtracting like terms.
Rewrite terms containing a radicand that is raised to a power and has a common factor with the index. The rule is ^n√x^m = x^(m/n). For example, if you have ^4√x^12, this can be simplified to x^(12/4). Because 12 divided by 4 is 3, the simplified answer is x^3.
Remove radicals from the denominators of fractions by multiplying the numerator and denominator by the radical expression. For example, consider the problem x/√y. Multiply the fraction by √y/√y. The x times √y is x√y and √y times √y in the denominator equals √y^2, which is y. Therefore, the simplified form would be x√y/y.
Change the sign of any radical expression that you move across an equal sign. For example, if you have 5√a = 3√a + 6, you would move 3√a across the equal sign and change its sign to create the equation 5√a - 3√a = 6. This can be simplified to 2√a = 6. Because both sides are divisible by 2, the final answer would be √a = 3.