Question

Find the additive inverse of: \[\sqrt{5}\]

Answer 1

Hint: We can just find negation by putting negative sign (-) before the number given.

Complete step-by-step answer:
In the question we are asked to find the additive inverse of \[\sqrt{5}\].
At first we understand what is an additive inverse.
In mathematics the additive inverse of a number ‘a’ is a number, that when added to a, yields zero. This number is also known as opposite number, sign change or negatition. For a real number, it reverses its sign: the opposite to a positive number is negative number and vice versa. Zero is the additive inverse of itself.
The additive inverse is defined as its inverse element under the binary operation of addition, which allows a broad generalization to mathematical objects other than numbers. As for any inverse operation, double additive inverse has no effect: - (- x) = x.
For a number, generally the additive inverses are found out or calculated using multiplication by -1; that is \[-n=-1\times n\]. Examples: integers rational and real numbers.
Additive inverses are closely related to subtraction which can be viewed as an addition of the opposite:
\[a-b=a+\left( -b \right)\]
Conversely additive inverses can be thought of subtraction from zero:
\[-a=0-a\]
Hence, unary minus sign notation can be seen as a shorthand for subtraction with the “0” symbol omitted, although the correct typography there should be no space after unary “a”.
So the additive inverse of \[\sqrt{5}\] is ‘\[-\sqrt{5}\]’.
Hence, the answer is \[-\sqrt{5}\].

Note: We can find just by multiplying the given number by -1 or by subtracting from 0 to get the desired result or answer.