Question

How do you solve $\sqrt{x+4}=0?$

Answer 1

Hint: We will square the whole equation given to find the value of the unknown variable. We know that $\sqrt{{{x}^{2}}}=x.$ Then we will transpose the necessary terms from one side to the other side of the equation to get the value of the unknown variable.

Complete step by step solution:
Let us consider the given equation \[\sqrt{x+4}=0.\]
Now, we can see that the left-hand side of the equation contains the square root of $x+4.$
Since the unknown variable $x$ is located inside the square root, we need get rid of the square root from the equation in order to find the value of the variable $x.$
Now, we are going to square the whole expression to eliminate the square root and to find the value of the unknown variable $x.$
When we square the equation, we will get ${{\left( \sqrt{x+4} \right)}^{2}}={{0}^{2}}.$
Since ${{0}^{2}}=0,$ we will get ${{\left( \sqrt{x+4} \right)}^{2}}=0.$
We have already learnt that the square root and the square get cancelled when they act together. That can be written as $\sqrt{{{y}^{2}}}=y.$
So, we will get ${{\left( \sqrt{x+4} \right)}^{2}}=x+4.$
Now the given equation will become $x+4=0.$
In the next step, we are going to transpose $4$ from the left-hand side of the equation to the right-hand side.
So, we will get, $x=0-4.$
That is, $x=-4.$
Hence the solution of the given equation $\sqrt{x+4}=0$ is $x=-4.$

Note: We know that the solution of an equation always satisfies the equation. So, we can confirm if the obtained value of the unknown variable is true by applying the value in the equation. If we apply the value $x=-4$ in the given problem, we will get $\sqrt{x+4}=\sqrt{-4+4}=0.$