Question

What is the conjugate of $5$?

Answer 1

In this problem we need to write the conjugate of the given number. We know that conjugate the term which is produced by changing the sign of binomials mostly in the form of $a+\sqrt{b}$ or $a+bi$. But when we observe the given value, it is not a binomial and does not have two values. So, we will assume the given number as $a+\sqrt{b}$ or $a+bi$ after that we will reverse the sign that means we will place $-$ if the number has $+$ or vice versa to get the conjugate of the number.

Complete step-by-step solution:
Given number is $5$.
We can observe that a given value has only one digit and does not have any imaginary or square root symbols. So, we are going to assume the given number as
$5=5+\sqrt{0}$
We all know that the value of $\sqrt{0}=0$. So, there will be no change in the given value.
We have the positive sign in the number $5+\sqrt{0}$. So, to get the conjugate of the number we are going to replace the positive sign with negative sign in the value $5+\sqrt{0}$, then we will get
$5-\sqrt{0}$
We can use the value $\sqrt{0}=0$ in the above equation, then we will have
$5-\sqrt{0}=5$
Hence the conjugate of the given number $5$ is $5$.

Note: Conjugate the numbers are very useful in simplifying the fractions which are having the root numbers or imaginary numbers as denominators. We will simplify the fraction by multiplying and dividing with conjugate number then applying the algebraic formula $\left( a+b \right)\left( a-b \right)={{a}^{2}}-{{b}^{2}}$.