Radicals Explanation Math

Introduction to Radicals explanation math:
Radical explanation math symbol (v), a symbol used to indicate the square root or nth root ,  Radical of an algebraic group, a concept in algebraic group theory  Radical of an ideal, an important concept in abstract algebra  Radical of a ring, in ring theory, a branch of mathematics, a radical of a ring is an ideal of "bad" elements of the ring.                                                      
(Source: wikipedia)

Examples for Radicals Explanation Math:

Addition for radicals explanation math:

Example 1:

Find the value of 25v3 +75 v3

Solution:

=v3 (25+ 75)
=100v3

Here the root is square root, only take the base are same so that we can add the roots easily.

So the result is =100v3

Example 2:

Find the value of 44v11 +77 v23+22v11 +66 v23

Solution:

= v11 (44+22)+ v23 (66+77)

= v11 (66)+ v23 (143)

= 66 v11 + 143 v23

Here the root is square root, the base are same in different terms so that we can add the roots easily.

So the result is =66 v11 + 143 v23

Examples for different radicals explanation math:

Example for square root:

v3 = 1.732

v25 = 5

v7 =  2.64

v12 = 3.46                              

Practice Problem for Radicals Explanation Math:

Multiplication for radicals explanation math:

Example 1:

Solution:

To find multiplication of v3x . v4y2    

= v(12 x y2)            

=  v12x y2   

The result is =  2yv3x   

Both the radicals have an same index of two, so we are multiply mutually under one radical keeping the 2 as its index number.

Example 2:

Solution:

To find multiplication of v(25xy2). v5   

= v(125 x y2)            

= 5yv5 x

The result is 5yv5 x

Both the radicals have an same index of two, so we are multiply mutually under one radical keeping the 2 as its index number.

Factorization for radical radical explanation math:

Example 1:

To find the value of v75

v75 = v5*3*3

= 3v5

The result is v75 = 3v5

Example 2:

To find the value cube root of v125

Cube root of  (v125) = v5*5*5

= 5

The result is v125 = 5

In a cube root of 125, here we take three out of one.

Example 3:

To find the value fourth root of v625

Fourth root of  (v625) = v5*5*5*5

= 5

The result is v625 = 5

In a fourth root of 625, here we take four out of one. Similar to all radicals