What is the square root of 181 in between?

Answer 1

Hi Mahoghany,

It sounds like you are asking which two whole numbers (0,1,2,3,4...) the square root of 181 lies in between. If this is the case we can determine the answer by looking at our perfect squares (2²=4, 3²=9, 4²=16, 5²=25, etc.). We can find our answer by looking at the square just before 181 and the square immediately after 181.

You may have memorized that 12²=144 but we do not want to assume that that is the value immediately before 181 (there may be another square greater than 144 and less than 181), the next greatest square would be 13² which you may not have memorized but some quick multiplication gives us 169 as our equivalent value. Indeed, 169 is closer to and less than 181 so it looks like it may be part of our answer. Let's continue by considering our next value of 14² which is equal to 196. It seems we have our answer.

169 and 196 are the closest perfect squares immediately less than and greater than 181. This same statement in equation form looks like this: 169 < 181 < 196. Since the question is asking for square roots let's square root all of those values to attain 13 < √181 < 14.

So although we may not know the exact value of √181 we know it should be in between 13 and 14.

Hope this helps!