Here we are  going to learn how to solve equations with radical signs.

• In order to remove radical sign first we have to take square root on both sides of the equation
• The square root and square will get canceled.
• By solving the equation, we can get the value of the variable.

Let us see some examples based on the above concept.

Example 1 :

Solve √(v - 4)  =  3

Solution :

√(v - 4)  =  3

In order to remove square root of the left side, we have to take squares on both sides.

[√(v - 4)]²  =  3²

v - 4  =  9

v - 4 + 4  =  9 + 4

v  =  13

Example 2 :

Solve

Solution :

Take square root on both sides

[(x/10)]²  =  [(3x - 58)]²

(x/10)  =  3x - 58

Multiplying by 10 on both sides

10 x (x/10) = 10 (3x - 58)

x = 30x - 580

Subtract by 30x on both sides

x - 30x  =  30x - 30x - 580

-29 x  =  -580

Divide by 29 on both sides

-29x/(-29)  =  -580/(-29)

x  =  20

Example 3 :

Solve

Solution :

Take square root on both sides

[(3n + 12)]²  =  [(n + 8)]²

3n + 12  =  n + 8

Subtract by 12 on both sides

3n + 12 - 12  =  n + 8 - 12

3n  =  n - 4

Subtract by n on both sides

3n - n  =  n - 4 - n

2n  =  -4

Divide by 2 on both sides

2n/2  =  -4/2

n  =  -2

Example 4 :

Solve

Solution :

Take square root on both sides

[(11- x)]²  =  [(x - 7)]²

11 - x  =  x - 7

Subtract by x on both sides

11 - x - x  =  x - x - 7

11 - 2x  =  -7

Subtract by 11 on both sides

11 - 2x - 11 =  -7 - 11

-2x  =  -18

Divide by -2 on both sides

-2x/(-2)  =  -18/(-2)

x  =  9

Example 5 :

Solve

Solution :

Take square root on both sides

[(x - 4) - (x)]²  =  (-2)²

[√(x - 4)]² + [√(x)]² - 2√(x - 4)√(x)   =  4

x - 4 + x - 2√x(x - 4)  =  4

2x - 4 - 2√(x²- 4x)  =  4

2x - 4 + 4 - 2√(x²- 4x)  =  4 + 4

2x - 2√(x²- 4x)  =  8

Subtract by 2x on both sides

-2√(x²- 4x)  =  8 - 2x

Divide by -2 on both sides

√(x²- 4x)  =  -4 + x

taking squares on both sides

[√(x²- 4x)]²  = [ -4 + x]²

x²- 4x  =  (-4)² + 2(-4) x + x²

x²- 4x  =  16 - 8 x + x²

Subtract by x² on both sides

x²- 4x -   =  16 - 8 x + x² -

-4x  = 16 - 8x

Add by 8x on both sides

-4x + 8x = 16 - 8x + 8x

4x  =  16

Divide by 4 on both sides

4x/4  =  16/4

x  =  4

After having gone through the stuff given above, we hope that the students would have understood "Solve radical equations".

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