How To Solve Radical Equations

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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.

 Examples of radical equation: -

         √(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
 
 

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