## Operations with Square Roots

Within the radical, divide by Functions Variations Quiz: Factor variables. All right reserved. You can do more than just simplify radical expressions.

Use the Quotient Raised to a Power Rule to rewrite this expression. Then, take the opposite of 9. The answer is: Remember that exponents only refer to the quantity immediately to their left unless a grouping symbol is used. When raising a power to a power, you multiply the exponents, but the bases have to be the same.

When the bases and the exponents are different we have to calculate each exponent and then multiply:. Method 2. Only if you are reversing the simplification process. Show Solution Find the cubes that surround Include your email address to get a message when this question is answered. Next, simplify the numbers under the radicals by looking for perfect squares or multiples of the numbers under the radicals that are perfect squares.

See the wikiHow article Simplify a Square Root. Did this summary help you?

Yes, though it's best to convert to exponential form first. The square root of a perfect square will be an integer. Visit Our Profiles. To do this, multiply the numbers as if they were whole numbers. An approach to handling roots that are not perfect squares, cubes, etc.

The simplified form is. Then click the button to compare your answer to Mathway's. All terms under the radicand are always positive, so you will not have to worry about sign rules when multiplying radicands.

You can break 25 down into its factors, 5 x 5, and move one 5 out of the square root sign to simplify the expression. As long as the roots of the radical expressions are the same, you can use the Product Raised to a Power Rule to multiply and simplify. Multiplication and Division.

### Operations with Square Roots

For any numbers a and b and any integer x: This article was co-authored by our trained team of editors and researchers who validated it for accuracy and comprehensiveness. Hence sqrt 5. We will combine this with the square root of a product rule in our next example to simplify an expression with three variables in the radicand. Since you are looking for the cube root, you need to find factors that appear 3 times under the radical.

A perfect square is the result of multiplying an integer a positive or negative whole number by itself.