SIMPLIFYING RADICALS WORKSHEET

About "Simplifying Radicals Worksheet"

Simplifying Radicals Worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on simplifying radicals. 

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Simplifying Radicals Worksheet - Problems

Problem 1 :

Simplify the expression : 

√20

Problem 2 :

Simplify the expression : 

√121

Problem 3 : 

Simplify the expression : 

√52

Problem 4 :

Simplify the expression : 

√45

Problem 5 :

Simplify the expression : 

√72

Problem 6 :

Simplify the expression : 

√40

Problem 7 : 

Simplify the expression : 

√27

Problem 8 :

Simplify the expression : 

√243

Problem 9 : 

Simplify the expression : 

√288

Problem 10 :

Simplify the expression : 

√320

Simplifying Radicals Worksheet - Solutions

Problem 1 :

Simplify the expression : 

√20

Solution : 

Decompose 20 into prime factors using synthetic division. 

So, we have

√20  =  √(2 ⋅ 2 ⋅ 5)

√20  =  2√5

Problem 2 :

Simplify the expression : 

√121

Solution : 

Decompose 121 into prime factors.

√121  =  √(11 ⋅ 11)

√121  =  11

Problem 3 : 

Simplify the expression : 

√52

Solution : 

Decompose 52 into prime factors using synthetic division.

So, we have

√52  =  √(2 ⋅ 2 ⋅ 13)

√52  =  2√13

Problem 4 :

Simplify the expression : 

√45

Solution : 

Decompose 45 into prime factors using synthetic division.

So, we have

√45  =  √(5 ⋅ 3 ⋅ 3)

√45  =  3√5

Problem 5 :

Simplify the expression : 

√72

Solution : 

Decompose 72 into prime factors using synthetic division.

So, we have

√72  =  √(2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3)

√72  =  2 ⋅ 3 ⋅ √2

√72  =  6√2

Problem 6 :

Simplify the expression : 

√40

Solution : 

Decompose 40 into prime factors using synthetic division.

So, we have

√40  =  √(2 ⋅ 2 ⋅ 2 ⋅ 5)

√40  =  2√(2 ⋅ 5)

√40  =  2√10

Problem 7 : 

Simplify the expression : 

√27

Solution : 

Decompose 27 into prime factors using synthetic division.

So, we have

√27  =  √(3 ⋅ 3 ⋅ 3)

√27  =  3√3

Problem 8 :

Simplify the expression : 

√243

Solution : 

Decompose 243 into prime factors using synthetic division.

So, we have

√243  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

√27  =  3 ⋅ 3 ⋅ √3

√27  =  9√3

Problem 9 : 

Simplify the expression : 

√288

Solution : 

Decompose 288 into prime factors using synthetic division.

So, we have

√288  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3)

√288  =  2 ⋅ 2 ⋅ √(2 ⋅ 3)

√288  =  4√6

Problem 10 :

Simplify the expression : 

√320

Solution : 

Decompose 320 into prime factors using synthetic division.

So, we have

√320  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5)

√320  =  2 ⋅ 2 ⋅ 2 ⋅ √5

√320  =  8√5

After having gone through the stuff given above, we hope that the students would have understood, "Simplifying Radicals Worksheet". 

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