On this webpage "radical expressions examples" we are going to see example problems of using radical expression.

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. **

To simplify a number which is in radical sign we need to follow the below steps

- Split the number as much as possible

- If two same numbers are multiplying in the square root sign,we need to take only one number from the radical sign.

- In case we have any number in front of radical sign already,we have multiply the number taken out by the number in front of radical sign already.

- If we have cube root ∛ or fourth root ∜ like that we have to take one term from 3 same terms or four same terms respectively.

Let us see a example problem to understand this method.

Simplify To reduce this number to the simplest form,we need to split this number as much as possible. √72 = √(2 x 2 x 2 x 3 x 3) |

= 6√2

So,the simplified value of √72 is 6√2.

In case we have any number in front of radical sign ,we have to combine the recent number taken out from the radical sign by the old number in front of radical sign already.

Simplify 3 √48

So,the simplified value of 3√48 is 12√3.

Now let us see the next example of the topic "radical expression examples".

Simplify by combining like radical terms:

We can add or subtract only like radical terms.Like radical term means a number which is in the root sign must be same but the number outside the radical may change.

For example,5√2 and 3√2 are like radical terms.Here the number inside the radical is same.

**Problem 1:**

Simplify the following radical expression

√27 + √75 + √108 - √48

**Solution:**

= √27 + √75 + √108 - √48

First we have to split the given numbers inside the radical as much as possible.

= √(3 x 3 x 3) + √(3 x 5 x 5) +

√(3 x 3 x 2 x 2 x 2) - √(2 x 2 x 2 x 2 x 2)

= 3 √3 + 5 √3 + 2 x 3 √2 - 2 x 2 √2

= 3 √3 + 5 √3 + 6 √2 - 4 √2

= (3 + 5) √3 + (6-4) √2

= 8 √3 + 2 √2

Now let us see the next example of the topic "radical expressions examples".

**Problem 2:**

Simplify the following radical expression

7 √30 + 2 √75 + 5 √50

**Solution:**

= 7 √30 + 2 √75 + 5 √50

First we have to split the given numbers inside the radical as much as possible.

= √(5 x 2 x 3) + √(5 x 5 x 3) + √(5 x 5 x 2)

Here we have to keep √30 as it is.

= √30 + 5 √3 + 5 √2

Now let us see the next example of the topic "radical expressions examples".

**Problem 3:**

Simplify the following radical expression

√27 + √105 + √108 + √45

**Solution:**

= 3 √5 + 2√95 + 3√117 - √78

First we have to split the given numbers inside the radical as much as possible

= √(3 x 3 x 3) + √(5 x 3 x 7) +

√(3 x 3 x 3 x 2 x 2) - √(5 x 5 x 3)

= 3 √3 + √105 + 3 x 2 √3 - 5 √3

= 3 √3 + √105 + 6 √3 - 5 √3

= (3 + 6 - 5) √3 + √105

= 4 √3 + √105

Now let us see the next example of the topic "radical expressions examples".

**Problem 4:**

Simplify the following radical expression

√45 + 3 √20 + √80 - 4 √40

**Solution:**

= √45 + 3 √20 + √80 - 4 √40

First we have to split the given numbers inside the radical as much as possible.

= √(3 x 3 x 5) + √(2 x 2 x 5) +

√(5 x 2 x 2 x 2 x 2) - √(5 x 2 x 2 x 2)

= 3 √5 + 2 √5 + 2 x 2 √5 - 2 √(2 x 5)

= 3 √5 + 2 √5 + 4 √5 - 2 √10

= (3 + 2 + 4) √5 - 2 √10

= 9 √5 - 2 √10

Now let us see the next example of the topic "radical expressions examples".

**Problem 5:**

Simplify the following radical expression

3√5 + 2√95 + 3√117 - √78

**Solution:**

= 3 √5 + 2√95 + 3√117 - √78

First we have to split the given numbers inside the radical as much as possible

= 3 √5 + 2 √(5 x 19) + 3 √(3 x 3 x 13) - √(3 x 2 x 13)

= 3 √5 + 2 √95 + 3 x 3 √13 - √78

= 3 √5 + 2 √95 + 9 √13 - √78

Now let us see the next example of the topic "radical expressions examples".

**Problem 6:**

Simplify the following radical expression

3 √32 - 2√8 + √50

**Solution:**

= 3 √32 - 2 √8 + √50

First we have to split the given numbers inside the radical as much as possible.

= 3 √(2 x 2 x 2 x 2 x 2) - 2 √(2 x 2 x 2) + √(5 x 5 x 2)

= (3 x 2 x 2 )√2 - (2 x 2) √2 + 5 √2

= 12 √2 - 4 √2 + 5 √2

= (12 + 5 - 4) √2

= 13 √2

Now let us see the next example of the topic "radical expressions examples".

**Problem 7:**

Simplify the following radical expression

2 √12 - 3√27 - √243

**Solution:**

= 2 √12 - 3 √27 - √243

First we have to split the given numbers inside the radical as much as possible.

= 2 √(2 x 2 x 3) - 3 √(3 x 3 x 3) - √(3 x 3 x 3 x 3 x 3)

= (2 x 2) √3 - (3 x 3) √3 - (3 x 3) √3

= 4 √3 - 9 √3 - 9 √3

= ( 4 - 9 - 9 ) √3

= -14 √3

Now let us see the next example of the topic "radical expressions examples".

**Problem 7:**

Simplify the following radical expression

√54 - √2500 - √24

**Solution:**

= √54 - √2500 - √24

First we have to split the given numbers inside the radical as much as possible.

= √(2 x 3 x 3 x 3) - √(5 x 5 x 5 x 5 x 2 x 2) -

√(3 x 2 x 2 x 2)

= 3 √(3 x 2) - (5 x 5 x 2) - (2 x 2) √(2 x 3)

= 3 √6 - 50 - 4 √6

= (3 - 4) √6 - 50

= -√6 - 50

Now let us see the next example of the topic "radical expressions examples".

**Question 9**

Simplify the following radical expression

√45 - √25 - √80

**Solution**

= √(5 x 3 x 3) - √(5 x 5) - √(5 x 2 x 2 x 2 x 2)

= 3 √5 - 5 - 2 x 2√5

= 3 √5 - 5 - 4√5

= -√5 - 5

Now let us see the next example of the topic "radical expressions examples".

**Problem 10:**

Simplify the following radical expression

5√95 - 2√50 - 3√180

**Solution**

= 5 √95 - 2 √50 - 3 √180

First we have to split the given numbers inside the radical as much as possible.

= 5 √95 - 2 √(2 x 5 x 5) - 3 √(3 x 3 x 2 x 2 x 5)

= 5 √95 - (2 x 5) √2 - (3 x 2 x 3 )√5

= 5 √95 - 10 √2 - 18 √5

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

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