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## Algebra 1

### Course: Algebra 1>Unit 11

Lesson 3: Simplifying square roots

## What are exponent properties?

We can use these properties of exponents help us to simplify expressions involving exponents:
Product rule: x, start superscript, a, end superscript, times, x, start superscript, b, end superscript, equals, x, start superscript, a, plus, b, end superscript. For example, x, squared, times, x, cubed, equals, x, start superscript, 5, end superscript.
Power rule: left parenthesis, x, start superscript, a, end superscript, right parenthesis, start superscript, b, end superscript, equals, x, start superscript, a, b, end superscript. For example, left parenthesis, x, squared, right parenthesis, cubed, equals, x, start superscript, 6, end superscript.
Quotient rule: start fraction, x, start superscript, a, end superscript, divided by, x, start superscript, b, end superscript, end fraction, equals, x, start superscript, a, minus, b, end superscript. For example, start fraction, x, start superscript, 5, end superscript, divided by, x, squared, end fraction, equals, x, cubed.
Zero exponent rule: x, start superscript, 0, end superscript, equals, 1. For example, 7, start superscript, 0, end superscript, equals, 1.

A radical is a symbol that we use to write square roots, cube roots, and other roots. For example, square root of, 81, end square root is the square root of 81, or the number we can multiply by itself to get 81. Another example is cube root of, 8, end cube root, which is the cube root of 8, or the number we can multiply by itself to get 8.
Practice with our Square roots exercise.
Practice with our Cube roots exercise.

## What are some common ways to simplify square roots?

One common way to simplify square roots is to factor the radicand (the number inside the square root symbol) into perfect squares. For example, square root of, 50, end square root can be simplified by factoring 50 into 25 times 2:
square root of, 50, end square root, equals, square root of, 25, times, 2, end square root, equals, square root of, 25, end square root, times, square root of, 2, end square root, equals, 5, square root of, 2, end square root

## Want to join the conversation?

• There's a mistake on this page where it says "the cubed root of 8 is the number we can multiply by itself to get 8". It should actually say the number we can multiply by itself 3 times to get 8 (because it's the cubed root, not the square root)
• there is mistake! it say the cubed root of 8s is the number we can multiply by itself to get 8! it should say the number we can multiply by itself 2 times to get 8! this is because it the cubed root! not the square root
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