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.

## How to simplify a radical number?

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.

## How to simplify radicals with large numbers?

 Example :Simplify √72 to the simplest formTo 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.

## How to simplify radicals with numbers on the outside?

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:

√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:

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:

√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:

√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:

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:

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:

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:

√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

√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:

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

## Related topics

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6