**Solving radical equations with radicals on both sides worksheet :**

Here we are going to see some practice questions on solving radical equations with radicals on both sides.

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

(1) Solve the following equation.

5√2 = √x

(2) Solve the following equation.

3√7 = √-y

(3) Solve the following equation.

√(3x + 12) = 3√3

(4) Solve the following equation.

√(x - 5) = 2√6

(5) Solve the following equation.

√(3x - 4) = √6

**Question 1 :**

Solve the following equation.

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

**Question 2 :**

Solve the following equation.

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

**Question 3 :**

Solve the following equation.

√(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

**Question 4 :**

Solve the following equation.

√(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

**Question 5 :**

Solve the following equation.

√(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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