## puzzle

Discussions concerned with knowledge of measurement, properties, and relations quantities, theoretical or applied.

### puzzle

I would very much appreciate an answer, and an explanation of how it was arrived at.
uninfinite
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### Re: puzzle

Trick question?? 5, rounded off, of course.

Watson
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### Re: puzzle

Watson » July 25th, 2017, 2:20 pm wrote:Trick question?? 5, rounded off, of course.

Incorrect.

That would give you sqrt (5+15 = 20) = 4.4721 plus (sqrt of 5 =) 2.23 = 6.7
uninfinite
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### Re: puzzle

I mean 5....squared, then times -1. ??

Watson
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### Re: puzzle

Google syndication appears to have pulled the image, so you may have to find another link, or just type in the equation. If the edit window closes, LMK, and I can paste it in.

Braininvat

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### Re: puzzle

x = 30.99705

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### Re: puzzle

Braininvat » July 25th, 2017, 6:35 pm wrote:Google syndication appears to have pulled the image, so you may have to find another link, or just type in the equation. If the edit window closes, LMK, and I can paste it in.

Soz BV - but I only have the vaguest impression of what any of all that means. Seems the image is still there - so if you fixed it, thank you. Speaking of things I don't know anything about: seems the site is not overwhelmed with mathematicians keen to share their insights.

I honestly have no idea how to begin to tackle this question. I know what a square root is - but I just cannot approach the task. I'm more interested in the explanation of how someone who does maths would work it out than what the answer might be. (If there is one!)

Clicking on the link - on an advert featured on this site, you might have thought would be one way to discover the answer. But no.
uninfinite
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### Re: puzzle

Don't hold me to that, I've was stung by a scorpion last night, worked out in the desert sun all day, and just finished a cheap bottle of sauvignon blanc.

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### Re: puzzle

uninfinite » July 25th, 2017, 2:43 pm wrote:I honestly have no idea how to begin to tackle this question. I know what a square root is - but I just cannot approach the task. I'm more interested in the explanation of how someone who does maths would work it out than what the answer might be. (If there is one!)

First find the square root of 15. Then find the difference of 15 - the square root of 15. Divide the difference by two. Square the quotient.

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### Re: puzzle

Incorrect. Rounding error. x = 31.7541634486

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### Re: puzzle

I was right the first time.

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### Re: puzzle

Drunk math is silly.

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### Re: puzzle

I got 49, just solving algebraically.

hint: start with squaring both sides, then start expanding , then you will end up squaring again to clean out the remaining square roots. Eventually, you get x on one side and easy peasy.

Braininvat

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### Re: puzzle

The real easy way is to figure it's the kind of problem where x + 15 is likely to be a perfect square and then survey in your mind the first few perfect squares. You land on 64 right away and realize 49 will give you that for the first term, and it's pretty intuitive from there.

Braininvat

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### Re: puzzle

I was thinking square root of 15 + the square root of x would be the same as that of 15 and x, why doesn't that work?

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### Re: puzzle

it obviously doesn't, but why?

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### Re: puzzle

BV, Thank you!
uninfinite
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### Re: puzzle

Brilliant Biv.

Like you I solved it by trial and error. I tried 5 squared, but the additions were too low, then 6 squared, and 7 squared worked (49).

But I'm darned if I can recall the algebraic steps. Squaring both sides of the equation just does not work. I tried a more elementary set of figures using 7 instead of 15 in my model - the square root of (x+7) plus the square root of (x) = 7. Obviouisly x = 9. But I'm annoyed that I can't work out any algebraic method to determine that x = 9.

It's driving me nuts.

doogles
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### Re: puzzle

It's still a broken image for me. Is there an updated link?
someguy1
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### Re: puzzle

Oh I see I turned off my ad blocker and now it's there.
someguy1
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### Re: puzzle

I do hope that I'm not spoiling the challenge for others, but it looked as if the thread was disappearing into oblivion.

The solution is in how to do binomials, which I hadn't done since year 10, 70 years ago.

(a + b) x (a + b) = a-squared + 2ab + b-squared
(a - b) x (a - b) = a-squared - 2ab + b-squared

doogles
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### Re: puzzle

actually, one should specify they do not wish x to be 0.
(obviously, the square root of 0+15 + the square root of 0 is the square root of 15).

Secondly, if all these all have to be integers, then one should suspect that x = n², and that x+15 = n²+2n+1
so that sqrt(x+15) = sqrt(n+1)² = n+1.
Then, n+1 + n = 15 leads quite easily to n=7 and x=49.

neuro
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### Re: puzzle

Good day to you neuro.

I found this puzzle intriguing for some weird reason and had to recall stuff I'd never used for decades. I was quite pleased with myself that I was still able to re-hash the old algebra.

I had a look at your first statement and felt that there was no need to specifically exclude zero as x, because it just does not fit the equation. By my calculation, it comes up with the incorrect answer that the sqrt15 = 15, which is obviously not balanced.

I found your second notion just as big a puzzle. "Secondly, if all these all have to be integers, then one should suspect that x = n², and that x+15 = n²+2n+1 so that sqrt(x+15) = sqrt(n+1)² = n+1. Then, n+1 + n = 15 leads quite easily to n=7 and x=49."

It works quite well and looks quite neat from x+15 = n²+2n+1. But for the life of me, I can't see where you obtained this equation from the original puzzle.

I used your notion to substitute x with n=squared and came up with the orthodox algebra, which, by the way handles fractions as well as integers.

But I can't see the steps that eliminated 15 from the right side of the equation to achieve (n-squared + 2n + 1). Is it possible to elaborate this neuro. I feel so dumb.

doogles
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### Re: puzzle

I am sorry for the mistake: you are right, x=0 is not a solution.

as for (x+15) = n²+2n+1, this simply comes from the assumption we are dealing with integers: if sqrt(x+15) is an integer, then it can be expressed as sqrt(x+15) = n+1, and x+15=n²+2n+1...

neuro
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