# Solving surd equations

We also need to be able to solve equations that involve surds.

## Example 1: **Surd equations**

**Question**

Solve for :

**Answer**

**Write in exponential notation**

**Divide both sides of the equation by 5 and simplify**

**Simplify the exponents**

**Check the solution by substituting the answer back into the original equation**

## Example 2: **Surd equations**

**Question**

Solve for :

**Answer**

**Factorise**

**Solve for both factors**

The zero law states: if , then or .

Therefore

or

**Check the solution by substituting both answers back into the original equation**

If :

If :

**Write the final answer**

The solution to is or .

## Example 3: **Surd equations**

**Question**

Solve for :

**Answer**

**Write the equation with only the square root on the left hand side**

Use the additive inverse to get all other terms on the right hand side and only the square root on the left hand side.

**Square both sides of the equation**

**Check the solution by substituting the answer back into the original equation**

If :

**Write the final answer**

The solution to is .

## Exercise 1: **Solving surd equations**

Solve for the unknown variable (remember to check that the solution is valid):