Square Root Function Problems

In general, square root of an integer A is a number B such that B2 = A, and we also deliver it by another ways, a number B whose square is A. Every non-unenthusiastic real number A has a only one of its kind of non-unenthusiastic square root, is said to be as the principal square root root, defined by a square roots symbol as sqrt (x). For positive (+) A, the principal square root will also rewrite in exponent notation, as like A1/2. For e.g. Principal square root of 16 is 4, obtained by sqrt (16) = 4, because 42 = 4 × 4 = 16 and 4 is non-negative.

Different Functions of Square Root:

Square root in math having different properties they are described below,

General expression with exponent and radical: `(^nsqrt (a) ^m) =(^nsqrt (a)) ^m =(a1/n) ^m = a^m/n`

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

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

Square Root Function Problem:

Example for square root in math: Add: `(9 xx sqrt (5))-(6 xx sqrt (5)) + (8 xx sqrt (5))`

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

`(9 - 6 + 8) xx sqrt (5)`

`(17 - 6) xx sqrt (5)`

After adding together, we get the answer like,

`11 xx sqrt (5)`

Example for square root function:   Simplify `sqrt (81) + sqrt (9)`

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

`sqrt (9 xx 9) + sqrt (3 * 3)`

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

`sqrt (9) xx sqrt (9) + sqrt (3) xx sqrt (3)`

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

`= 9 + 3`

Simplify by adding like terms to get the answer

`= (9 + 3)`

`= 12`

Thus, `sqrt (81) + sqrt (9) = 12.`

Example for square root function: Solve `sqrt (2) xx sqrt (196) = sqrt (392)`

` = sqrt (2 xx 196)`

`= sqrt (2 xx 14^2)`

` = ^14 sqrt (2)`

Practice problem for square root function:

Problem for square root function: `(sqrt (121))`

Answer: `11`

Problem for square root function: `(sqrt (169))`

Answer: `13`

Problem for square root function: `(sqrt (2025))`

Answer: `45`

Problem for square root function: `sqrt (2) + sqrt (4)`

Answer: `2 sqrt (2)`