# HOW TO SIMPLIFY RADICAL EXPRESSIONS

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

## How to simplify radical expressions?

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

Step 1:

Split the numbers in the radical sign as much as possible

Step 2:

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

Step 3:

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.

Step 4:

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.

Step 5:

Let us see a example problem to understand this method.

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:

√27 + 5 √75 + √108 -3 √48

Solution:

= √27 + 5 √75 + √108 - 3 √48

First we have to split the given numbers inside the radical as much as possible.  =  3 √3 + 25 √3 + 6 √3 - 4 √3

= (3 + 25 + 6 - 4) √3

= 30 √3

Now let us see the next example of the topic "how to simplify radical expressions".

Problem 2:

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 "how to simplify radical expressions".

Problem 3:

√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 "how to simplify radical expressions".

Problem 4:

√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 "how to simplify radical expressions".

Problem 5:

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 "how to simplify radical expressions".

Problem 6:

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 "how to simplify radical expressions".

Problem 7:

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 "how to simplify radical expressions".

Problem 7:

√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 "how to simplify radical expressions".

Question 9

√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 "how to simplify radical expressions".

Problem 10:

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

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