# How To Solve Radical Equations

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

Definition: - When equations contain a root then it is known as a radical equation. It can be square root, cube root, fourth root, … , nth root.

√(4 x + 1) = √ x
√ (x ^ 2 – 10 x + 25) = 0
√ x = 2
√ ( x – 3) + √ (2 x + 5) – 8 = 0

Question 1: - Solve √(x + 1) = √ x

Solution: -
i)             Square both sides of the equation,
√ (4 x + 1) = √ x
(4 x + 1) = x
ii)            Subtract from both sides of the equation,
(4 x + 1) – 1 = x -1
4 x = x – 1
iii)            Subtract x both sides
4 x - x = (x – 1) – x
3 x = - 1
iv)           Divide both sides by 3.
3 x / 3 = - 1/ 3
x = - 1/ 3

Question 2: - Solve √ (x ^ 2 – 10 x + 25) = 0.

Solution: -
√ (x ^ 2 – 10 x + 25) = 0
Or,       √(x^2 – 2 * x * 5 + 5^2) = 0
Or,       √ (x – 5) ^2 = 0
Or,        (x – 5) = 0
Or,         x = 5
Therefore x = 5.

Question 3: - Find the value of x: √ x = 2

Solution: -
√ x = 2
Or, x = 2 ^2
Or, x = 4
Therefore x = 4