Question

What is the square root of infinity and the square root of zero?

Answer 1

Hint : In this question, we need to define the outcome of the square root of infinity and zero. An operation that, when applied to a number returns the value that when multiplied by itself gets the number given. We take the square root of the value to be positive because there are no real numbers that when multiplied together give you a negative number.

Complete step by step solution:
In the given question,
By solving the square root of infinity and the square root of zero.
We perform an operation that, when executed on a number gives the value that when multiplied by itself returns the number given. They take the form where $x$ is the number on which the operation is being performed.
The square of infinity can be expressed as the following limit, we can get
$\mathop {\lim }\limits_{x \to \infty } \sqrt x = + \infty$
Hence, the square root of infinity is infinity.
we know that,
$\infty \cdot \infty = \infty$
Hence, we conclude the same answer.
The square of zero can be expressed as the following limit, we can get
$\mathop {\lim }\limits_{x \to 0} \sqrt x = 0$
Since, The square root of zero is $0$. Because, a square can only be positive or negative, negative numbers do not have real square roots.
Therefore, The limit of the square root of zero is zero.

Note : It is important to note that if you are limited to real-number values, the number you are taking the square root of must be positive because there are no real numbers that when multiplied together give you a negative number. The limit of the square root of zero is zero.