Frequently asked questions about exponents & radicals
What are exponent properties?
We can use these properties of exponents help us to simplify expressions involving exponents:
Product rule: . For example, .
Power rule: . For example, .
Quotient rule: . For example, .
Zero exponent rule: . For example, .
Practice with our Multiply & divide powers (integer exponents) exercise.
Practice with our Powers of products & quotients (integer exponents) exercise.
What are radicals?
A radical is a symbol that we use to write square roots, cube roots, and other roots. For example, is the square root of , or the number we can multiply by itself to get . Another example is , which is the cube root of , or the number we can multiply by itself to get .
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, can be simplified by factoring into times :
Practice with our Simplify square roots exercise.
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)(29 votes)
- Radicals are radical. B)(15 votes)
- 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(9 votes)
- Micheal B Jordan is the goat at basketball(3 votes)
- does size really matter?(3 votes)
- help me I have a high school entrance exam soon, what should I study to get a good score?(2 votes)
- Can I find out which perfect squares I use to fully simplify and replace the radicand? For example, the square root of 160 could be simplified like 2 and the square root of 40, but the fully simplified answer is 4 to the square root of 10.(1 vote)