**Add and subtract radical expressions worksheet :**

Here we are going to see some practice questions on adding and subtracting radical expressions.

(1) Simplify the radical expression given below

√3 + √12

(2) Simplify the radical expression given below

√75 - √25

(3) Simplify the radical expression given below

√7 + √49

(4) Simplify the radical expression given below

√5 + 2√5 - 5√5

(5) Simplify the radical expression given below

√5 + 3 √7 - 4 √5 - 5 √7

(6) Simplify the radical expression given below

3√3 + 4 √3 - √2

(7) Simplify the radical expression given below

2(√5 - √3) + 3(√3 - √5)

(8) Simplify the radical expression given below

√8 + √18

(9) Simplify the radical expression given below

√12w + √27w

(10) Simplify the radical expression given below

√45t^{3} + √25t^{3}

**Question 1 :**

Simplify the radical expression given below

√3 + √12

**Solution :**

= 3 √3

Hence 3 √3 is the answer.

**Question 2 :**

Simplify the radical expression given below

√75 - √25

**Solution :**

= √75 - √25

Here the given two radical terms are not like radicals. Let us split the numbers inside the radical as much as possible.

= √(5 x 5 x 3) - √(5 x 5)

= 5 √3 - 5

**Question 3 :**

Simplify the radical expression given below

√7 + √49

**Solution :**

= √7 + √49

Since 7 is prime number, we cannot split this hereafter. We can split 49.

= √7 + √(7 x 7)

= √7 + 7

**Question 4 :**

Simplify the radical expression given below

√5 + 2√5 - 5√5

**Solution :**

= √5 + 2√5 - 5√5

Since √5 is common for all three terms, we are going to take √5 commonly from all the terms and simplify the numbers.

= (1 + 2 - 5) √5

= (3 - 5) √5

= -2 √5

**Question 5 :**

Simplify the radical expression given below

√5 + 3 √7 - 4 √5 - 5 √7

**Solution :**

= √5 + 3 √7 - 4 √5 - 5 √7

Now we have to group the like radicals.

= √5 - 4 √5 + 3 √7 - 5 √7

= (1 - 4) √5 + (3 - 5) √7

= - 3 √5 - 2 √7

**Question 6 :**

Simplify the radical expression given below

3√3 + 4 √3 - √2

**Solution :**

= 3√3 + 4 √3 - √2

The first two terms are having √3. Hence they are like radicals, we can combine them.

= (3 + 4) √3 - √2

= 7 √3 - √2

**Question 7 :**

Simplify the radical expression given below

2(√5 - √3) + 3(√3 - √5)

**Solution :**

= 2(√5 - √3) + 3(√3 - √5)

Distribute 2 for (√5 - √3) and distribute 3 for (√3 - √5).

= 2√5 - 2√3 + 3√3 - 3√5

Now we have to combine the like terms

= 2√5 - 3√5 - 2√3 + 3√3

= (2 - 3)√5 + (-2 + 3)√3

= -1√5 + 1√3

= -√5 + √3

**Question 8 :**

Simplify the radical expression given below

√8 + √18

**Solution :**

= √8 + √18

We can split 8 and 18 as much as possible to get factors.

= √(2 x 2 x 2) + √(2 x 3 x 3)

= 2√2 + 3√2

= (2 + 3) √2

= 5 √2

**Question 9 :**

Simplify the radical expression given below

√12w + √27w

**Solution :**

= √12w + √27w

We can split 12 and 27 as much as possible to get factors.

= √(2 x 2 x 3 x w) + √(3 x 3 x 3 x w)

= 2√(3 x w) + 3√(3 x w)

= 2√3w + 3√3w

= (2 + 3)√3w

= 5√3w

**Question 10 :**

Simplify the radical expression given below

√45t^{3} + √25t^{3}

**Solution :**

= √45t^{3} + √20t^{3}

We can split 45 and 25 as much as possible to get factors.

= √(3 x 3 x 5 x t^{3}) + √(2 x 2 x 5 x t^{3})

= 3 t √5t + 2 t√5t

= (3 t + 2t) √5t

= 5t √5t

- Properties of radicals
- Simplifying radical expressions worksheets
- Square roots
- Ordering square roots from least to greatest
- Operations with radicals
- How to simplify radical expressions

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