How can I prove every positive real number has square root? Does it ask that we can express any positive real number as square root of something? like 4 is equal to square root of 16?

$f(x)=x^2$ from $[0,\infty)\to [0,\infty)$ is a strictly increasing continuous function,since $f(0)=0$ and $\lim_{x\to\infty}f(x)=\infty$ the function is bijective,hence it's inverse is also bijective since $\sqrt{x}$ is the inverse that implies it's also surjective.This is true if the definition of square root is such that it is the inverse of the square function.
