## SIMPLIFY RADICAL EXPRESSIONS USING THE DISTRIBUTIVE PROPERTY WORKSHEET

Simplify radical expressions using the distributive property worksheet :

The method of multiplying the radical terms which are added or subtracted inside the bracket by the common radical term or numerical value outside the bracket is know as distributive property.

## Simplify radical expressions using distributive property worksheet - Practice questions

(1)  Simplify the radical expression given below

√3(√3 + √12)

(2)  Simplify the radical expression given below

-√2(-4 -√2)

(3)  Simplify the radical expression given below

√2(7 + √5)

(4)  Simplify the radical expression given below

2(√4 + √10)

(5)  Simplify the radical expression given below

√5(√8 + √10)

(6)  Simplify the radical expression given below

√3(√9 + √21)

(7)  Simplify the radical expression given below

2√5(√6 + 2)

(8)  Simplify the radical expression given below

√14x(3 - √2x)

(9)  Simplify the radical expression given below

√21x(5 + √7)

(10)  Simplify the radical expression given below

(5 - √3(5 + √3)

## Simplify radical expressions using the distributive property worksheet - Solution

Question 1 :

Simplify the radical expression given below

√3(√3 + √12)

Solution :

Hence the answer is 9.

Let us look into the solution of next problem on "Simplify radical expressions using the distributive property worksheet".

Question 2 :

Simplify the radical expression given below

-√2(-4 -√2)

Solution :

=  -√2(-4 -√2 )

Distribute -√2 inside the bracket.

=  -√2(-4) -√2 (-√2 )

For every two same numbers which are multiplying inside the radical sign, we can take one number commonly from the radical.

=  4√2 + 2

Hence the answer is 4√2 + 2.

Let us look into the solution of next problem on "Simplify radical expressions using the distributive property worksheet".

Question 3 :

Simplify the radical expression given below

√2(7 + √5)

Solution :

=  √2(7 + √5)

Distribute √2 inside the bracket.

=  √2(7) + √2 (√5)

=  7√2 + √(2x5)

=  7√2 + √10

Hence the answer is 7√2 + √10

Question 4 :

Simplify the radical expression given below

2(√4 + √10)

Solution :

=  2(√4 + √10)

=  2 (√4) + 2 (√10)

=  2 (√(2 x 2) + 2 √10

=  (2 x 2) + 2 √10

=  4 + 2 √10

Hence the answer is 4 + 2 √10

Question 5 :

Simplify the radical expression given below

√5(√8 + √10)

Solution :

=  √5(√8 + √10)

=  √5 (√8) + √5 (√10)

=  √(5 x 8) + √(5 x 10)

=  (√(5 x 2 x 2 x 2) + √(5 x 5 x 2)

=  2(√(5 x 2) +  5√2

= 2√10 +  5√2

=  4 + 2 √10

Hence the answer is 4 + 2 √10

Question 6 :

Simplify the radical expression given below

√3(√9 + √21)

Solution :

= √3(√9 + √21)

=  √3 (√9) + √3 (√21)

=  √(3 x 9) + √(3 x 21)

=  (√(3 x 3 x 3) + √(3 x 3 x 7)

=  3√3 +  3√7

Hence the answer is 3√3 +  3√7

Question 7 :

Simplify the radical expression given below

2√5(√6 + 2)

Solution :

=  2√5(√6 + 2)

=  2√5 (√6) + 2√5(2)

=  2√(5 x 6) + 2√(5 x 2)

=  2√30 + 2√10

Hence the answer is 2√30 + 2√10

Question 8 :

Simplify the radical expression given below

√14x(3 - √2x)

Solution :

=  √14x(3 - √2x)

=  √14x (3) - √14x(√2x)

=  √42x  - √(14 ⋅ 2 ⋅ x ⋅ x)

=  √42x  - √(2 ⋅ 7 ⋅ 2 ⋅ x ⋅ x)

=  √42x  - 2x√7

Hence the answer is √42x  - 2x√7

Question 9 :

Simplify the radical expression given below

√21x(5 + √7)

Solution :

=  √21x(5 + √7)

=  √21x (5) + √21x (√7)

=  5√21x  + √(21 ⋅ x ⋅ 7)

=  5√21x  + √(3 ⋅ 7 ⋅ x ⋅ 7)

=  5√21x  + 7√3x

Hence the answer is  5√21x  + 7√3x

Question 10 :

Simplify the radical expression given below

(5 - √3(5 + √3)

Solution :

=  (5 - √3(5 + √3)

=  5(5) + 5√3 - 5√3 - √3√3

=  25 - √(3 ⋅ 3)

=  25 - 3

=  22

Hence the answer is  22

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