Monday, April 15, 2013

Square Root in Math

Introduction to square root in math:

In math, we use a radical symbol which is known as square root. Square root is also said to be as radical and the radical symbol is (sqrt). Rubicund is referred to a number which is present inside the root (i.e. sqrt (x), here x is referred as rubicund). Square root math is deals with the different properties of expressing square root by using various calculations. Let us see what properties of square root in math briefly.

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Different properties of square root in math:



Different properties of square root in math are described below,

General expression with exponent and radical:

`^nsqrt (a) ^m`   =`(^nsqrt (a)) ^m`   = (`a1/n) ^m ` = `am/n`

Multiplication property for radical expression: `^nsqrt (ab)` = `(^nsqrt (a))` ` (^nsqrt (b))`

Division property for radical expression: `(^nsqrt (a/b))` = `(^nsqrt (a))` / `(^nsqrt (b))`

Example for square root in math:


Example for square root in math: Add: `(8 * sqrt (2))` `-` `(6 * sqrt (2)) ` `+ ` `(9 * sqrt (2))`

Solution: Unite like terms by adding together the numerical coefficients.

`(8 - 6 + 9) * sqrt (2)`

` (17 - 6) * sqrt (2)`

After adding together, we get the answer like,

` 11 * sqrt (2)`

Answer: `(8 * sqrt (2))-(6 * sqrt (2)) + (9 * sqrt (2)) = 11 * sqrt (2)`

Example for square root in math:   Simplify, `sqrt (64)` `+ ` `sqrt (8)`

Solution: Take the given question and split the terms like,

`Sqrt (4 * 16)` `+ ` `sqrt (2 * 2 * 2)`

Rewrite the square root by using product of square root theorem.

`sqrt (4) * sqrt (16)` `+ ` `sqrt (2) * sqrt (2) * sqrt (2)`

`sqrt (2)* sqrt (2)* sqrt (4)* sqrt (4) ` `+` `sqrt (2) * sqrt (2) * sqrt (2)`

To simplify even further we use the definition of square root,

`(2 * 4) + 2(sqrt (2))`

Simplify by adding like terms to get the answer.

`(8 + 2(sqrt (2)))`

Simplify: `sqrt (64) + sqrt (8) = (8 + 2(sqrt (2)))`

Practice problem for square root in math:

Example for square root in math:` (^3sqrt (729))`

Answer: cubic root of (729) = `9^3`

Example for square root in math: `(^4sqrt (1296))`

Answer: fourth root of (1296) = `6^4`

Example for square root in math: `(sqrt (1225))`

Answer: (sqrt (1225))= 35

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