Simplest Radical Form

Simplest radical form is defined as the reduction of value in radical or radicand itself or simply the radicals. The symbol of the radical is v. In this simplest form of radicals, the square root, cube roots, 4th root is not present. Let us see the example here n is the root index, x is the radicand and v is the radical symbol. Let we see about the simplest form of radical with example problem.
Example Problems - Simplest Radical Form:

Example 1:

Write the following in the simplest form of radical.

a) `root(4)(256)`   b) `sqrt(169)`   c) `root(3)(640)`   d) `sqrt(140)`

Solution:

a) `root(4)(256)`

= `root(4)(16 * 16)`

We know that 16 is the perfect square of 4.

= `root(4)(4 * 4* 4* 4)`  =  4

Answer: `root(4)(256)`

b)`sqrt(169)`

= `sqrt(13 * 13)`  = 13

Answer: `sqrt(169)`  = 13

c) `root(3)(640)`

= `root(3)(4 * 4 * 4 * 10)`   = 4 `root (3)(10)`

Answer: `root(3)(640)`  =  4 `root (3) (10)`

d)  `sqrt(140)`

= `sqrt(7 * 2 * 2 * 5)`  =  2`sqrt(7 * 5)` = 2`sqrt(35)`

Answer:  `sqrt(140)``sqrt(35)`

Example 2:

Which of the following is the simplest form of the radical `root(3)(250)`

a) 5 * 2

b) 5 `sqrt(2)`

c)  3 `sqrt(2)`

d) 5 and 3

Answer: b = 5 `root (3 ) (2)`

Exaplanation:

Solution:

250 can multiply by 5 * 5 * 5 * 2.

`root(3)(250)`  = `root(3)(5 * 5 * 5 * 2)`

`root(3)(250)`     =  5`root (3) (2)`

Now u clear the simplest radical form  `root(3)(250)`  is 5 `root (3) (2)` Hence the correct option is b that is 5 `root (3) (2)`

Answer:  `root(3)(250)`     =  5`root (3) (2)`

Example 3:

Write the simplest radical form of `root(4)(6^(5))`

Solution:

We know the 6^5 is 6 * 6 * 6 * 6 * 6. and also it can write 6^4 + 6

`root(4)(6^(5))`     =  `root(4)(6^(4) * 6 ^ (1))`

`root(4)(6^(5))` =`root(4)(6^(4))`   `root (4 ) (6)`

`root(4)(6^(5))`  = 6 `root ( 4 ) (6)`

Answer: `root(4)(6^(5))`  = 6 `root (4) (6)` These are example problems in simplest radical form. Let we do the practice problem of simplest radical form.
Practice Problem - Simplest Radical Form:

1. What is the simplest radical form of the number `root(3)(27)` .

Answer: 3

2. What is the simplest form of radicals `root(4)(20 + 20 + 8)` .

Answer:  2`root (4) (3)`

Now clear about the simplest of radical and to reduce the radical form.