**Solve radical equations :**

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

Add 4 on both sides

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

Add 4 on both sides

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 - x² = 16 - 8 x + x² - 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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