Root 3 Value

Introduction of root 3 value:

Root is the form of method in the radical, which has been used in mathematics. The radical form has been given as root √. In which the root radical symbol root "√" or otherwise `root(2)(x)` . The numerical significance inside the radical symbol or root symbol called as the radicand. There are many methods available in the rooting analysis they are, square root, cube root, fourth root and its up-to nth root. Here we are going to see about  root 3 value using the formula method and the example problems and practice problems related to the root.

Properties of Roots:

The product of two Variables in the roots which are in different variables in the root, it can be written with in a single root into as a product of those two rooted variables.
`"sqrt(x) xx` =`sqrt((x)(y))`     (By the First property)

The variable at the outside the root symbol, when it gets into root, it turns into a square of that value.
`(x)sqrt(y)` = `sqrt((x^2)(y))` ` (By the Second Property)`

In division, root of the whole division which can be written as a individual roots, as root in numerator with root separately and in denominator with root separately.
`sqrt((x)/(y))` = `sqrt(x)/sqrt(y)`        (By the Third property)

The number without the square value within the root as the result. It is because, When a perfect square value comes out of the root symbol.
`sqrt4` = 2     (By the Fourth Property)

Root 3 Value - Example Problems:

Root 3 value - Problem:

Calculate the root value 3

Solution:

The square root value for 3 is nearly equal value to the square values between 1 and 2, because 12 = 1  and 22 = 4

Step 1: Divide 3 by 1.

`3 / 1 ` = 3

Step 2: Take average for 3 and 1.

` (3 +1) / 2 ` = 2

Step 3: Divide 3  by 2

` 3 / 2 ` =  1.5

Step 4: Take average for the 1.5 and  2

`(1.5 + 2)/2 ` =  1.75

Step 5: Now check the result by taking square for that value.

1.75 2 =  3.0625

If the value is not equal to the requested value then repeat the steps  4, 3 and 5.

Step 6: Divide 3 by 1.75

`3/ 1.75` =  1.71428571

Step 7: Take average for 1.75 and  1.71428571

(1.71428571+ 1.75)/2 = 1.73214285

Step 8: Now check the result by taking square for that value.

1.73214285 2 =  3.00031885

This value is very closer to the given root value `sqrt (3) `

If the value is not equal to the requested value then repeat the steps  4, 3 and 5.Please express your views of this topic Operations on Rational Numbers by commenting on blog.

Root 3 Value - Practice Problems:

Problem 1:

Calculate the root value for 33

Answer: `sqrt 33` =  5.74456265

Problem 2:

Calculate the value for 333

Answer: `sqrt 333` =  18.2482876