# SIMPLIFYING RADICAL EXPRESSIONS WORKSHEET

Simplifying Radical Expressions Worksheet :

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

Before look at the worksheet, if you would like to know the basic stuff about simplifying radical expressions,

## Simplifying Radical Expressions Worksheet - Problems

Problem 1 :

Simplify the radical expression :

√169 + √121

Problem 2 :

Simplify the radical expression :

√20 + √320

Problem 3 :

Simplify the radical expression :

√117 - √52

Problem 4 :

Simplify the radical expression :

√243 - 5√12 + √27

Problem 5 :

Simplify the radical expression :

-√147 - √243

Problem 6 :

Simplify the radical expression :

(√13)(√26)

Problem 7 :

Simplify the radical expression :

(3√14)(√35)

Problem 8 :

Simplify the radical expression :

(8√117) ÷ (2√52)

Problem 9 :

Simplify the radical expression :

(8√3)2

Problem 10 :

Simplify the radical expression :

(√2)3 + √8 ## Simplifying Radical Expressions Worksheet - Solutions

Problem 1 :

Simplify the radical expression :

√169 + √121

Solution :

Decompose 169 and 121 into prime factors using synthetic division.

 √169  =  √(13 ⋅ 13)√169  =  13 √121  =  √(11 ⋅ 11)√121  =  11

So, we have

√169 + √121  =  13 + 11

√169 + √121  =  24

Problem 2 :

Simplify the radical expression :

√20 + √320

Solution :

Decompose 20 and 320 into prime factors using synthetic division. √20  =  √(2 ⋅ 2 ⋅ 5)√20  =  2√5 √320  =  √(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5)√320  =  2 ⋅ 2 ⋅ 2 ⋅ √5√320  =  8√5

So, we have

√20 + √320  =  2√5 + 8√5

√20 + √320  =  10√5

Problem 3 :

Simplify the radical expression :

√117 - √52

Solution :

Decompose 117 and 52 into prime factors using synthetic division. √117  =  √(3 ⋅ 3 ⋅ 13)√117  =  3√13 √52  =  √(2 ⋅ 2 ⋅ 13)√52  =  2√13

So, we have

√117 - √52  =  3√13 - 2√13

√117 + √52  =  √13

Problem 4 :

Simplify the radical expression :

√243 - 5√12 + √27

Solution :

Decompose 243, 12 and 27 into prime factors using synthetic division. √243  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)  =  9√3

√12  =  √(2 ⋅ 2 ⋅ 3)  =  2√3

√27  =  √(3 ⋅ 3 ⋅ 3)  =  3√3

So, we have

√243 - 5√12 + √27  =  9√3 - 5(2√3) + 3√3

Simplify.

√243 - 5√12 + √27  =  9√3 - 10√3 + 3√3

√243 - 5√12 + √27  =  2√3

Problem 5 :

Simplify the radical expression :

-√147 - √243

Solution :

Decompose 147 and 243 into prime factors using synthetic division. √147  =  √(7 ⋅ 7 ⋅ 3)  =  7√3

√243  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)  =  9√3

So, we have

-√147 - √243  =  -7√3 - 9√3

-√147 - √243  =  -16√3

Problem 6 :

Simplify the radical expression :

(√13)(√26)

Solution :

Decompose 13 and 26 into prime factors.

13 is a prime number. So, it can't be decomposed anymore.

√26  =  √(2 ⋅ 13)  =  √2 ⋅ √13

So, we have

(√13)(√26)  =  (√13)(√2 ⋅ √13)

(√13)(√26)  =  (√13 ⋅ √13)√2

(√13)(√26)  =  13√2

Problem 7 :

Simplify the radical expression :

(3√14)(√35)

Solution :

Decompose 14 and 35 into prime factors.

√14  =  √(2 ⋅ 7)  =  √2 ⋅ √7

√35  =  √(5 ⋅ 7)  =  √5 ⋅ √7

So, we have

(3√14)(√35)  =  3( √2 ⋅ √7)(√5 ⋅ √7)

(3√14)(√35)  =  3(√7 ⋅ √7)(√2 ⋅ √5)

(3√14)(√35)  =  3(7)√(2 ⋅ 5)

(3√14)(√35)  =  21√10

Problem 8 :

Simplify the radical expression :

(8√117) ÷ (2√52)

Solution :

Decompose 117 and 52 into prime factors using synthetic division. √117  =  √(3 ⋅ 3 ⋅ 13)√117  =  3√13 √52  =  √(2 ⋅ 2 ⋅ 13)√52  =  2√13

(8√117) ÷ (2√52)  =  8(3√13) ÷ 2(2√13)

(8√117) ÷ (2√52)  =  24√13 ÷ 4√13

(8√117) ÷ (2√52)  =  24√13 / 4√13

(8√117) ÷ (2√52)  =  6

Problem 9 :

Simplify the radical expression :

(8√3)2

Solution :

(8√3)=  8√3 ⋅ 8√3

(8√3)2  =  (⋅ 8)(√3 ⋅ √3)

(8√3)2  =  (64)(3)

(8√3)2  =  192

Problem 10 :

Simplify the radical expression :

(√2)3 + √8

Solution :

(√2)3 + √8  =  (√2 ⋅ √2  √2) + √(2⋅ ⋅ 2)

(√2)3 + √8  =  ( √2) + 2√2

(√2)3 + √8  2√2 + 2√2

(√2)3 + √8  =  4√2 After having gone through the stuff given above, we hope that the students would have understood, "Simplifying Radical Expressions Worksheet".

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