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How to Solve Radical Equations

UserMark time28 November,2014

Solving Radical Equations

An equation with a square root or a cube root is usually called radical equation. Square root of any number is simply that number multiplied by itself once. Cube root of a number is that number multiplied by itself three times. A radical equation is therefore an equation with a square root or a cube root. In order to solve radical equations we need to get rid of the square roots and cube roots.

  • Square roots equations: Here, you isolate the square root on one side of the equation. Then square both sides of the equation.

Here is an example:                                                            √ (2x + 9) – 5= 0

Step 1

Isolating the square root on left hand side of the equation you get,

√ (2x + 9) = 5

Step 2

Squaring both sides you get,

2x + 9 = 25

Step 3

Solve it like a simple equation.

2x = 25 – 9

2x = 16

X = 8

Got it?

  • Cube root equations: In cube root equations, you solve the equation by cubing both sides of the equation rather than square rooting it.

Step 1

Cube both sides of the equation.

3√(2x-5 ) = 3

Step 2

Cubing both sides we get,

(3√(2x-5))3 = 33

2x -5 = 27

2x = 27 + 5

2x = 32

x = 16

  • If you are unsure whether your answer is correct or not there is a simple way to check. Just put the number instead of the variable and see whether it is correct or not. For instance,

∛(2x-5)= 3

                                          ∛(2×16-5) = 3                (Here x= 16)

∛(32-5)= 3

∛27 = 3

3 = 3

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