Question

What is the square root of infinity

Answer 1

»» HI FRIEND !!! »»

¥ CLEAR EXPLANATION ¥

— Square root of infinity is : Infinity only there is no other value or number to replace....!!

Infinity means nothing.....

Infinity is a symbol which anything can't replaced in that place ....

Any root either it may cube root / square root / any number if it is infinity then it is un defined value we can in simple words....!!!

★ HOPE THIS HELPS U BUDDY !!!! ★

Answer 2

Then the square root of infinity is not a real number and it must lie on the extended real line, so it must be infinity. Q.E.D.). A more interesting result - at least in general - are limits. You can study the behaviour of functions like the square root as goes to infinity.


As others have pointed out, the issue here is that the square root functions is not defined for infinite. f(x)=x−−√f(x)=x is only defined for x∈R+x∈R+and infinite is not in this set (in more advanced maths, you can have f:R→Cf:R→C, i.e. have the square roots take inputs from the whole real line, including negative numbers and spit out numbers in the complex plane, but this extension doesn’t solve our problem).

Some could argue that in some sense infinite is a number (you can use it to denote a - poorly defined and impossible to reach, granted - quantity, and isn’t it what numbers are for, after all?), and for the limited cases in which this is relevant in maths, the extended real line has been invented (it’s a funny concept really: it’s an infinite line with uncountably many points on it, and at both ends of it lie “numbers” which can never be reached). Still, the output of a function defined on the extended real line would necessarily be on the extended real line, so the result would be a rather uninteresting ∞−−√=∞∞=∞ (by way of contradiction, suppose this is not true: then there exists a real number as such that ∞−−√=a∞=a, but since square root is a continuous, strictly increasing function we know that there exists a unique positive real number - it’s not particularly insightful to prove this with the whole real line, we just need they positive half-line and positive infinity -, b=a2b=a2 such that b√=ab=a; then we have ∞=b∈R+∞=b∈R+. Since infinity is not a real number, we reach a contradiction. Then the square root of infinity is not a real number and it must lie on the extended real line, so it must be infinity. Q.E.D.).

A more interesting result - at least in general - are limits. You can study the behaviour of functions like the square root as xx goes to infinity. This allows you to deal with infinity without using the cumbersome extended real line and allows you to say things like “∞−−√∞ goes to infinity as x goes to infinity”. Not quite its value (cause, as said, in its conventional definition it doesn’t have a value ), but close enough for practical purposes I would say!


MAY THIS HELP U MY FRND!!!!!!