SOLUTION: In this investigation, you will be estimating the values of and to the nearest hundredths place. (this numbers I need the square root) (√40 √75 √90 √245 √450 √640

Question 1161965: In this investigation, you will be estimating the values of and to the nearest hundredths place.
(this numbers I need the square root) (√40 √75 √90 √245 √450 √640 √675 )
1. Describe clearly what strategy you plan to use to estimate these values.

Reflect on the calculations you made. What general methods or short cuts did you find to make the calculations easier as you did each calculation?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I'll do one of these; you can figure out the rest.

Consider

. What is the largest perfect square that is less than 90? And what is the smallest perfect square that is larger than 90?

and

, respectively. So, since:

we can say

Since 90 is pretty close to the middle of the 81 to 100 interval, 9.5 is a pretty good initial guess for the square root of 90.

A little bit too large, so let's try 9.4

A lot too small compared to our first guess, but now we know that.

Since 9.5 squared is significantly closer to 90 than 9.4 squared, the next guess should be closer to 9.5 than 9.4. Let's try the value 9.47.

Close, but still a little small, so

We are still lower, but closer to the true value than our initial guess of 9.5, but now we know that:

Since we have seen that 9.49 is closer than 9.50 and you only have to get to the nearest hundredths place, 9.49 is your answer.

Checking the work we see that the calculator value is:

9.4868329805051379959966806332982 which rounds to 9.49. By the way, remember that the calculator value is still an approximation, albeit a much better one than the above process. But the square root of anything that is not a perfect square is an irrational number -- the decimal representation goes on forever and never repeats. The only way to represent the square root of 90 exactly is

John

My calculator said it, I believe it, that settles it

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