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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):











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