Question

Is 36 a solution of \(\sqrt{x}=-6 ?\) Why or why not?

Short answer

No, 36 is not the solution to the equation \(\sqrt{x}=-6\), because a square root cannot yield a negative number.

Step-by-step solution

Understand Properties of Square Root

We should recall that square root of any real number is always positive or zero but never negative. This is because when you square any real number, negative or positive, you always get a positive result or zero, never a negative result. So, the equation \(\sqrt{x}=-6\) does not have any real number solutions.

Substitute the Given Value

In the next step, substitute x = 36 into the equation \(\sqrt{x} = -6\) to see if both sides are equal, despite knowing already that it can't be a solution. If the results are equal, then 36 is a solution. Otherwise, it's not a solution.

Check if Both Sides are Equal

Calculating the square root of 36, we get \( \sqrt{36} = 6 \). Now compare both sides now and see that 6 is not equal to -6. Therefore, the value 36 is not a solution of the equation, \(\sqrt{x}=-6\).