Simple Radical Help

Introduction to simple radical help:

Simple radical help article deals with the definition of the radical and the model problem that help to understand the radical in math.

Definition of radical:

The number which has the radical symbol (square root) is said to be radical number. In radical numbers there are three parts, they are radicals, radical symbol and the index of the radical number.


Conditions that help in simple radical


When the radicals and index present in the both terms should be same, and then we can add the two terms.
When the radicals and index present in the both terms should be same, and then we can subtract the two terms.
When we multiply the two terms with same radicals then the square root symbol will be removed.
When we divide the two terms with same radicals then the two terms will be cancelled.

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Model problem that help to understand the radical in math.


Problem 1:

`2 sqrt 5+3 sqrt 5`

Solution:

Here the radicals present in the both terms are same, so we can add the two terms.

`2 sqrt 5+3 sqrt 5 = (2+3) sqrt 5`

=` 5 sqrt 5`

The answer is `5 sqrt 5`


Problem 2:

`2 sqrt 5-3 sqrt 5`

Solution:

Here the radicals present in the both terms are same, so we can subtract the two terms.

`2 sqrt 5-3 sqrt 5 = (2-3) sqrt 5`

= `-1 sqrt 5`

The answer is `-1 sqrt 5`

Problem 3:

`2 sqrt 2+ 3sqrt 8`

Solution:

We have to simplify `3sqrt8 = (3*2) sqrt 2`

Now it is

`2 sqrt 2 +6 sqrt 2`

= `(2+6) sqrt 2`

= `8 sqrt 2nbsp`

Problem 4:

`9 sqrt 2- 3sqrt 8`

Solution:

We have to simplify `3sqrt8 = (3*2) sqrt 2`

Now it is

`9 sqrt 2 -6 sqrt 2`

= `(9-6) sqrt 2`

= `3 sqrt 2`

Problem 5:

`4 sqrt 6 * (8 sqrt 6)`

Solution:

We have to multiply 4 and 8 individually and the sqrt 6 and sqrt 6 individually

`4 sqrt 6 * (8 sqrt 6) = (4*8)*(sqrt 6 *sqrt6)`

= 32*(6)

= 192

Problem 6:

`(4 sqrt 6 )/ (8 sqrt 6)`

Solution:

We have to divide  4 and 8 individually and the sqrt 6 and sqrt 6 individually

` (4 sqrt 6 )/ (8 sqrt 6) = (4/8)*(sqrt 6 /sqrt6)`

= `(1/2)*(1)`

= `1/2`