**How to solve radical equations with radicals on both sides :**

Here we are going to see how to solve radical equations with radicals on both sides.

In order to remove radical signs, we have to take squares on both sides.

**Example 1 :**

Solve the following equation and check the solution

5√2 = √x

**Solution :**

5√2 = √x

By taking squares on both sides, we get

(5√2)^{2} = √x^{2}

5^{2}√2^{2} = √x^{2}

25(2) = x

x = 50

**Example 2 :**

Solve the following equation and check the solution

3√7 = √-y

**Solution :**

3√7 = √-y

By taking squares on both sides, we get

(3√7)^{2} = ( √-y)^{2}

3^{2}√7^{2} = y

9(7) = y

y = 63

**Example 3 :**

Solve the following equation and check the solution

√(3x + 12) = 3√3

**Solution :**

√(3x + 12) = 3√3

By taking squares on both sides, we get

(√3x + 12)^{2} = (3√3)^{2}

3x + 12 = 3^{2}√3^{2}

3x + 12 = 9 (3)

3x + 12 = 27

Subtract 12 on both sides, we get

3x + 12 - 12 = 27 - 12

3x = 15

Divide by 3 on both sides

3x / 3 = 15/3

x = 5

**Example 4 :**

Solve the following equation and check the solution

√(x - 5) = 2√6

**Solution :**

√(x - 5) = 2√6

By taking squares on both sides, we get

(√(x - 5))^{2} = (2√6)^{2}

x - 5 = 2^{2}√6^{2}

x - 5 = 4 (6)

x - 5 = 24

Add 5 on both sides

x - 5 + 5 = 24 + 5

x = 29

**Example 5 :**

Solve the following equation and check the solution

√(3x - 4) = √6

**Solution :**

√(3x - 4) = √6

By taking squares on both sides, we get

(√(3x - 4))^{2} = (√6)^{2}

3x - 4 = √6^{2}

3x - 4 = 6

Add 4 on both sides

3x - 4 + 4 = 6 + 4

3x = 10

Divide by 3 on both sides

3x/3 = 10/3

x = 10/3

After having gone through the stuff given above, we hope that the students would have understood "How to solve radical equations with radicals on both sides".

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