## What is a Radical Function?

A radical function is any function that contains a variable inside a root. This includes square roots, cubed roots, or any nth root.

Examples:

f(x)=

This does not include funtions that only contain numerals inside radicals. An independent variable must lie inside the radical.

Examples of

Examples:

*y=√(x+3)**p=**√*(3q)+17f(x)=

*∜*(x-z)This does not include funtions that only contain numerals inside radicals. An independent variable must lie inside the radical.

Examples of

**non-radical**functions: f(x)=x+*√2*

y=x^2+3x+√5

y=x^2+3x+√5

## How Do You Solve Radical Equations?

A few simple steps can help you solve a function for a given value.

This is done by first isolating the radical on one side of the equation.

Then both sides of the equation are taken to the same power of the root. (eg. If there is a square root, you would square both sides).

This will remove the root and leave everything inside it untouched. (eg.

Then the remaining equation should be easy to solve using basic algebra.

Example 1:

First isolate the radical by subtracting 17 from both sides.

2-17=

-15=

Then square both sides.

(-15)^2=[

225=3q

Then solve for q by dividing both sides by 3.

225/3=3q/3

Simplify.

q=75

Example 2: 3=

Since the root is already isolated, we can just take both sides to the forth power.

3^4=

81=x-5

Once again we solve for x.

x=86

This is done by first isolating the radical on one side of the equation.

Then both sides of the equation are taken to the same power of the root. (eg. If there is a square root, you would square both sides).

This will remove the root and leave everything inside it untouched. (eg.

*(√*x*)^2=x*).Then the remaining equation should be easy to solve using basic algebra.

Example 1:

*2=**√*(3q)+17First isolate the radical by subtracting 17 from both sides.

2-17=

*√*(3q)+17-17-15=

*√*(3q)Then square both sides.

(-15)^2=[

*√*(3q)]^2225=3q

Then solve for q by dividing both sides by 3.

225/3=3q/3

Simplify.

q=75

Example 2: 3=

*∜*(x-5)Since the root is already isolated, we can just take both sides to the forth power.

3^4=

*[∜*(x-5)]^481=x-5

Once again we solve for x.

x=86