ADD AND SUBTRACT RADICAL EXPRESSIONS WORKSHEET





About "Add and subtract radical expressions worksheet"

Add and subtract radical expressions worksheet :

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

Add and subtract radical expressions worksheet - Practice questions

(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

√45t3 + √25t3

Add and subtract radical expressions - Solutions

Question 1 :

Simplify the radical expression given below

√3 + √12

Solution : 

  =  3 √3

Hence √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

√45t3√25t3

Solution : 

  =  √45t3√20t3

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

  =  √(3 x 3 x 5 x t3) + √(2 x 2 x 5 x t3)

  =  3 t √5t + 2 t√5t

  =  (3 t + 2t) √5t

  =  5t √5t

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