Talk about stating the obvious

[Square Wheels]

 

[Kirby]

He still didn't come up with a number at the end.  He should have just used a calculator.

[Wilbur ★]

16 hours ago, Square Wheels said:

 

No. This is why I went to a lesser school and had girlfriends.   

[donkpow]

This looks suspiciously like a question on statistics. While stating the obvious may be taboo, answering a statistical question is quite easy, obviously. 

[Ralphie ★]

16 hours ago, Kirby said:

He still didn't come up with a number at the end.  He should have just used a calculator.

Pretty pointless, eh? Simplest terms.  

[maddmaxx ★]

42

[MickinMD ★]

Actually, the problem is not to "solve" for a numerical answer, it's just to a simplified set of terms.

I looked at it and tried to approximately solve it. I knew the square root of 36 is 6, so the square root of 35 is just under 6.

So 30 x (35)^1/2 = 30 x (just under 6) = just under 180.  Note that "^1/2" means "square root."

So 220 - 30x(35)^1/2 = 220 - (a little less than 180) = a little more than 40.

So we're looking for the square root of a little more than 40.  The square root of 6, 36, is a little more than 4 away from just over 40 and the square root of 7, 49, is a little less than 9 away from just over 40.

"A little more than 4" is about halfway to "a little less than 9." so the answer is approximately halfway between 6 and 7 or 6 1/2 = 6.5

I actually did all that in my head before I wrote it down.

Now let me use a calculator, calculate the numerical values of the square roots, solve and see how close my approximation is to the actual numerical value:

(220 -30 (35)^1/2)^1/2 = (220 -30 (5.912608))^1/2 = (220 -177.482394)^1/2

= (42.5176065)^1/2 = 6.520553

OK, I was off by 0.020553 or a 0.316% error.

I would put complicated physics formulas on the board involving squares, cubes, square roots, etc., and do approximation calculations in my head while my high school physics students were using calculators to get the answer.  I'd tell them something like, "The answer is something like 14.8," and they'd be amazed when their calculations matched.

They were amazed because they grew up on calculators - I began to seriously use one my third year of college, when they became affordable and did more than add and subtract.  So I have an edge because I first had to estimate numbers, the same way people in the middle ages could hear an hour's tavern song about the news and, on one hearing, go home and sing the whole thing to their family: the printing press revolutionized learning but stole a lot of our memory.

When my gifted students would divide 20.12345 by 5.12345, push a wrong button on their calculators and get an answer something like 0.0023456, it wasn't so obvious to them that 20 divided by 5 is about 4 and can't be less than 1 because they were conditioned to plugging numbers into a calculator and accepting, without thinking whatever answer came up!

So I amazed them!

 

[2Far ★]

2 hours ago, MickinMD said:

Actually, the problem is not to "solve" for a numerical answer, it's just to a simplified set of terms.

I looked at it and tried to approximately solve it. I knew the square root of 36 is 6, so the square root of 35 is just under 6.

So 30 x (35)^1/2 = 30 x (just under 6) = just under 180.  Note that "^1/2" means "square root."

So 220 - 30x(35)^1/2 = 220 - (a little less than 180) = a little more than 40.

So we're looking for the square root of a little more than 40.  The square root of 6, 36, is a little more than 4 away from just over 40 and the square root of 7, 49, is a little less than 9 away from just over 40.

"A little more than 4" is about halfway to "a little less than 9." so the answer is approximately halfway between 6 and 7 or 6 1/2 = 6.5

I actually did all that in my head before I wrote it down.

Now let me use a calculator, calculate the numerical values of the square roots, solve and see how close my approximation is to the actual numerical value:

(220 -30 (35)^1/2)^1/2 = (220 -30 (5.912608))^1/2 = (220 -177.482394)^1/2

= (42.5176065)^1/2 = 6.520553

OK, I was off by 0.020553 or a 0.316% error.

I would put complicated physics formulas on the board involving squares, cubes, square roots, etc., and do approximation calculations in my head while my high school physics students were using calculators to get the answer.  I'd tell them something like, "The answer is something like 14.8," and they'd be amazed when their calculations matched.

They were amazed because they grew up on calculators - I began to seriously use one my third year of college, when they became affordable and did more than add and subtract.  So I have an edge because I first had to estimate numbers, the same way people in the middle ages could hear an hour's tavern song about the news and, on one hearing, go home and sing the whole thing to their family: the printing press revolutionized learning but stole a lot of our memory.

When my gifted students would divide 20.12345 by 5.12345, push a wrong button on their calculators and get an answer something like 0.0023456, it wasn't so obvious to them that 20 divided by 5 is about 4 and can't be less than 1 because they were conditioned to plugging numbers into a calculator and accepting, without thinking whatever answer came up!

So I amazed them!

 

Yeah, i got the “about” answer pretty simply. However, going through eleventyseven steps to make it “simpler” is what turns people off about math.