sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what about sqrt*1=1 ?

[Indranil]

why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?

 

[Dr.Peterson]

why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?

First, "sqrt" is not a number you can multiply ("*"). It is a function, so you write sqrt(x) to mean the square root of x.

The reason sqrt(4)*sqrt(4) = 4 is that the left hand side is (sqrt(4))^2, and by definition the square root is the inverse of squaring: that is, squaring undoes the square root. In general, (sqrt(x))^2 = x.

What is the square root of 1? By definition, it is the (non-negative) number whose square is 1. Since 1^2 = 1, we conclude that sqrt(1) = 1.

 

[pka]

why sqrt of 1 is 1?
As I know sqrt * 4 x sqrt * 4 = 4 because sqrt * 4 = 2, so 2 x 2 = 4 but what's about sqrt * 1?

To Indranil, You have been asked to use sqrt(x) which is standard function notation? Why don't you please do so?

If $\displaystyle a\ge 0$ then $\displaystyle sqrt(a)$ is real number having the property that $\displaystyle \left(\sqrt{a}\right)^2=a$
So $\displaystyle sqrt(1)\cdot sqrt(1)=\left(\sqrt{1}\right)^2=1$

 

[HallsofIvy]

If you are really asking "Why isn't it $\displaystyle \sqrt{1}= \pm 1$" its because $\displaystyle \sqrt{x}$ is a function and functions must return one value for every x. $\displaystyle \sqrt{x}$ is defined as "the positive number, a, such that $\displaystyle a^2= x$".