Radical Form in Math

Introduction to radical form in math:

Radicals is a form of symbol which is used in the mathematics. It is shown that the radical  symbol as  root "v". The number inside the radical symbol which is called as the radicand of the radical value, for example if the given value is square root of `sqrtx` . The x is called as the radicand which is the number inside the radical symbol root "v". There are more number of rooting methods available depending upon the value we have. The roots are square root `sqrtx` , cube root `root(3)(x)` , Fourth root `root(4)(x)` this up to nth root `root(n)(x)` . Here we are going to see about the radical form in math in different methods and the solved example problems on it.

Understanding How do you Simplify Radicals is always challenging for me but thanks to all math help websites to help me out.

Radical form in math - Some Properties:

Radicals form - Representations:

Function `a^(1/n)` :

The radical exponent  `a^(1/n) = root(n)(a)`

If n has odd value then,

If a is positive value then the function  `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is negative.

If a is zero value then the function `a^(1/n)` is also zero

If n has even value then,

If a is positive value then the function `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is not a real number.

If a is zero value then the function`a^(1/n)` is also zero

Radical Expression:

`x^(1/n) = root(n)(x)`    it is n root of x value.

Relation between expression and Radical:

`(x^(1/n))^n`   is the relation between the expression and radical .

Radical Exponent of Product:

`root(n)(axxb) = (axxb)^(1/n) = root(n)(a) xx root(n)(b) = a^(1/n) xx b^(1/n) `

Radical for a quotient:

`root(n)(a/b) = (a/b)^(1/n) = root(n)(a)/root(n)(b) = a^(1/n)/b^(1/n)`

Radical of a fraction:

`msqrta^n = a^(n/m) `


Radical form in math - Example Problems:


Radical form in math -  Problem 1:

Solve the radical form for 16.

Solution:

Method 1: Finding the square root of 16 by long division method

_4__
2)16 (
16
0
The value for the `sqrt 16` is 4

Method 2:

`sqrt16` = `sqrt(4^2)`

=` (4^2)^2`

= `(4)^(2/2)`

= 4

Radical form in math - Problem 2:

Solve radical value for 435

Solution:

The root value 435 is nearly equal to the square values between 20 and 21, because 202 = 225 and 212 = 256

Step 1: Divide 435 by 20.

`435 / 20` = 21.75

Step 2: Take average for 21.75 and 20.

` (21.75+20)/2 ` = 20.87500

Step 3: Divide 255 by 16

`435/20.87500 ` =  20.8383234



Step 4: Take average for the 20.8383234 and 20.87500

`( 20.8383234 + 20.87500)/2` =  20.8566617

Step 5: Now check the above result by taking square

20.8566617 2 =  435.000337

This value is more or less equal to 435

If the value is not equal repeat the step 3 and step 4

Is this topic Multiplicative Inverse hard for you? Watch out for my coming posts.

Radical form in math - Example Problems:


Problem 1:

Solve the radical value for 567

Answer: `sqrt 567` = 23.8117618

Problem 2:

Solve the radical val ue for 632

Answer: `sqrt 632` = 25.1396102

Adding Radicals Calculator

Introduction to adding radicals calculator:

Radicals:

The symbol used to indicate root of a number is known as radicals.  The square root, cube root can be expressed by using the radical symbol.  The radicals also mean that the root.  To understand the radicals, first we need to know about exponentiation. That is exponential xn = x * x * x * x …….n times x. The root of xn can be expressed as root (n)(x^n) = x .

The radical symbol is,

Fig(i) Radicals

Calculator:

A calculator is a small (often pocket-sized), usually inexpensive electronic device used to perform the basic operations of arithmetic.(source : Wikipedia).

Fig(ii) Adding radicals calculator

In this article we are going to learn about how to adding radicals using calculator.

Rules to Adding Radicals :

Before we get into problems , we need to know the rules for adding radicals.

Rules :

We can add the radicals with the same index and radicand . For example the radicals of index 2 can only add. We can add the radical of index 2 with the radical of index 3.

For example , `sqrt(4)` + `sqrt (4)` = ( 1 + 1) `sqrt(4)`

= 2 `sqrt(4)`

Let us see some problems on adding radicals by using calculator.

I am planning to write more post on Factorization Calculator, Equivalent Fractions Calculator. Keep checking my blog.

Problems on Adding Radicals Calculator:

Problem 1:

Add the radicals `5sqrt(36)` + `2sqrt(81) `

Solution:

Given, `5sqrt(36)` + `2sqrt(81) `

We need to add the given radicals.

Before that we can simplify the given radicals.

We know that, `root(n)(x^n) ` = x

`sqrt(36)` = `sqrt(6^2)` = 6

`sqrt(81)` = `sqrt(9^2) ` = 9

`5sqrt(36)` + `2sqrt(81)` = 5*6 + 2*9

= 30 + 18

= 48

Answer: 5`sqrt(36)` + 2`sqrt(81)` = 48

Problem 2:

Add the radicals `8sqrt(8)` + `sqrt(8) `

Solution:

Given, `8sqrt(8)` + `sqrt(8) `

We need to add the given radicals.

Before that we can simplify the given radicals.

We know that,` root(n)(x^n)` = x

`sqrt(8)` = `sqrt(4 * 2 )`

= `sqrt(4)` * `sqrt(2)`

= `sqrt(2^2)` * `sqrt(2)`

= `2sqrt(2)`

`sqrt(8)` = `2sqrt(2)`

8`sqrt(8)` + `sqrt(8)` = 8 * `(2sqrt(2)) ` + 2`sqrt(2)`

= 16 `sqrt(2)` + 2`sqrt(2)`

= (16 + 2)`sqrt(2)`

=  18`sqrt(2)`

Answer: 8`sqrt(8)` + ` sqrt(8) ` = 18`sqrt(2)`

Problem 3:

Add the radicals 3`root(3)(9)` + 2`root(2)(8) `

Solution:

Given,3`root(3)(9)` + 2`root(2)(8)`

We need to add the given radicals.

Here , given two radicals are has two different index as well as different radicand.

So we can add it further.

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