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How to Square Root Variables?

TopSquare root of a variable is represented by radical symbol “√”. This symbol is also known as Square root or simply root symbol. Square root of any variable 'a' is a number 'b' such that b2 = a. Then 'b' can be calculated as b = √ a. Square root is actually exponent 1 / 2. For instance, 7 is a square root of 49 for 72 = 49 or √49 = 7, 8 is the square root of 64 since 82 = 64 or √64= 8.

Square roots of 0, 1, 2 and 3 are √0 = 0, √1 = 1, √2 = 1.414 and √3 = 1.732. Square root can be applied to Fractions, whole Numbers, complex numbers, etc. Expressions which consist of radical or root symbol are known as radical expression. Square root is applicable to variables. Let us consider an example to see how to square root variables?

Assume that a, b and c are variables and radical expression consisting of a, b, and c is given as
√ (75 a5 b3 c2),
Let us solve it:
We know that 75 can be decomposed as 25 * 3,
Square root of 25 is 5. Thus √75 can be written as 5 √3.
Square root of a5 will be given as:
Sqrt (a * a * a * a * a) = sqrt (a2 * a2 * a),
= (a2) 1 / 2 * (a2) 1 / 2 * (a) 1 / 2,
Thus we can write Sqrt (a * a * a * a * a) = a * a * √ a = a 2 √ a,

Similarly when we solve square root of b3, it will be sqrt (b 3) = b √b
Square root of c2 will be sqrt (c2) = c,
sqrt (75 a5 b3 c2) = 25 a 2 b c √ 3ab.