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
Isolating the square root on left hand side of the equation you get,
√ (2x + 9) = 5
Squaring both sides you get,
2x + 9 = 25
Solve it like a simple equation.
2x = 25 – 9
2x = 16
X = 8
Cube root equations: In cube root equations, you solve the equation by cubing both sides of the equation rather than square rooting it.
Cube both sides of the equation.
3√(2x-5 ) = 3
Cubing both sides we get,
(3√(2x-5)) 3 = 3 3
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,
∛(2×16-5) = 3 (Here x= 16)
∛27 = 3
3 = 3
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