In this page simplifying radical expressions worksheet, we are going to see some practice questions.

A symbol used to indicate square of any number is called radical. The number which is under the root is called radicand.

√3 is called square root of 3

**Example 1 :**

Simplify **√**72 to the simplest form

**Solution :**

To reduce this number to the simplest form, we need to decompose this number as much as possible.

√72 = √(2 **⋅** 2 **⋅** 2 **⋅** 3 **⋅** 3)

= 2 **⋅** 3 √2

= 6 √2

Now we are going to see practice questions. In the solution page, you can find solution for each problems with detailed explanation. Once you understood the concept, you can try the next question on your own.

**Question 1 :**

Simplify the following radical expression

√27 + √75 + √108 - √48

(A) 2 √3 + √2 (B) 5 √3 + √2 (C) 8 √3 + 2 √2

**Question 2 :**

Simplify the following radical expression

7√30 + 2√75 + 5√50

(A) √30 + 5√3 + 5√2 (B) 5√3 + 5√2 (C) √30 + 5√2

**Question 3 :**

Simplify the following radical expression

√27 + √105 + √108 + √45

(A) 4√3 (B) 4√3 + √105 (C) √3-5√2

**Question 4 :**

Simplify the following radical expression

√45 + 3√20 + √80 - 4√40

(A) 9√5 - 2√10 (B) 11√15 (C) 9√5

**Question 5 :**

Simplify the following radical expression

3√5 + 2√95 + 3√117 - √78

(A) 2√95 + √78

(B) 2√95 + 9√13 - √78

(C) 3√5 + 2√95 + 9√13 - √78

**Question 6 :**

Simplify the following radical expression

3√32 - 2√8 + √50

(A) 9√2 (B) 13√2 (C) 3√2

**Question 7 :**

Simplify the following radical expression

2√12 - 3√27 - √243

(A) 4 √3 (B) 14 √3 (C) -14 √3

**Question 8 :**

Simplify the following radical expression

√54 - √2500 - √24

(A) -√6 - 50 (B) -5√6 - 50 (C) -2√6 - 5

**Question 9 :**

Simplify the following radical expression

√45 - √25 - √80

(A) - √5 - 3 (B) - √5 - 5 (C) - 2√5 + 5

**Question 10 :**

Simplify the following radical expression

5√95 - 2√50 - 3√180

(A) 5√95 - 10√2 - 18√5

(B) 5√95-18√5

(C) -10√2-18√5

- Different forms of numbers
- Properties of numbers
- Rationalizing the denominator
- Rationalizing Worksheet
- Radical

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