**Simplifying Radicals Worksheet :**

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

Before look at the worksheet, if you would like to know how to simplify radicals,

**Problem 1 :**

Simplify :

√20

**Problem 2 : **

Simplify :

√121

**Problem 3 : **

Simplify :

√52

**Problem 4 : **

Simplify :

√45

**Problem 5 : **

Simplify :

^{3}√72

**Problem 6 : **

Simplify :

^{3}√40

**Problem 7 : **

Simplify :

^{3}√27

**Problem 8 : **

Simplify :

^{4}√243

**Problem 9 : **

Simplify :

^{5}√288

**Problem 10 : **

Simplify :

^{6}√320

**Problem 1 :**

Simplify :

√20

**Solution : **

Decompose 20 into prime factors using synthetic division.

So, we have

√20 = √(2 ⋅ 2 ⋅ 5)

√20 = 2√5

**Problem 2 : **

Simplify :

√121

**Solution : **

Decompose 121 into prime factors.

√121 = √(11 ⋅ 11)

√121 = 11

**Problem 3 : **

Simplify :

√52

**Solution : **

Decompose 52 into prime factors using synthetic division.

So, we have

√52 = √(2 ⋅ 2 ⋅ 13)

√52 = 2√13

**Problem 4 : **

Simplify :

√45

**Solution : **

Decompose 45 into prime factors using synthetic division.

So, we have

√45 = √(5 ⋅ 3 ⋅ 3)

√45 = 3√5

**Problem 5 : **

Simplify :

^{3}√72

**Solution : **

Decompose 72 into prime factors using synthetic division.

So, we have

^{3}√72 = ^{3}√(2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 3)

^{3}√72 = 2 ⋅ ^{3}√(3 ⋅ 3)

^{3}√72 = 2 ⋅ ^{3}√(3 ⋅ 3)

^{3}√72 = 2^{3}√9

**Problem 6 : **

Simplify :

^{3}√40

**Solution : **

Decompose 40 into prime factors using synthetic division.

So, we have

^{3}√40 = ^{3}√(2 ⋅ 2 ⋅ 2 ⋅ 5)

^{3}√40 = 2^{3}√5

**Problem 7 : **

Simplify :

^{3}√27

**Solution : **

Decompose 27 into prime factors using synthetic division.

So, we have

^{3}√27 = ^{3}√(3 ⋅ 3 ⋅ 3)

^{3}√27 = 3

**Problem 8 : **

Simplify :

^{4}√243

**Solution : **

Decompose 243 into prime factors using synthetic division.

So, we have

^{4}√243 = √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3)

^{4}√243 = 3√3

**Problem 9 : **

Simplify :

^{5}√288

**Solution : **

Decompose 288 into prime factors using synthetic division.

So, we have

^{5}√288 = ^{5}√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3)

^{5}√288 = 2√3

**Problem 10 : **

Simplify :

^{6}√320

**Solution : **

Decompose 320 into prime factors using synthetic division.

So, we have

^{6}√320 = ^{6}√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 5)

^{6}√320 = 2√5

After having gone through the stuff given above, we hope that the students would have understood how to simplify radicals.

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