Estimating Square Roots - Problem 1

Here I’m asked to find each square root. I’m going to be really careful with the positive and negative signs.

Part a, the negative square root of 81. Well I know the square root of 81, principle solution would be 9 but so the square root of 81 with the negative in front if it will be -9. Be careful this one actually has no real solution because the negative value of 81 doesn’t have a real square root. No real solution, I’m going to abbreviate solution.

The square root of 1/16 that means what number or fraction in this case times itself gives me the answer 1/16. Well 16 is hopefully ringing bells in your head because 16 is equal to 4 times 4. That will help you figure out that ¼ times ¼ gives you 1/16. Notice I wrote the positive version of the principal square root because it didn’t specify as opposed to this guy. Here I’m going to have a positive and a negative answer.

This is kind of tricky because it’s a decimal. Think of this as a fraction if it helps you that’s equal to one 1/100 and then 100 is a square number. What number times itself gives you 100? Well 10. So that tells me that my answer here is going to be 1/10 and -1/10. If you want to you can write your answer as decimals 0.1 and -0.1. Those are equal that’s the fraction answer that’s the decimal answer.

So when you are asked to find square roots it’s not too hard as long as you know your perfect square numbers and please be really careful with the positive and negative signs, that becomes important as you move through your Math career.