## square root of 29,929?

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
Motherof8
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### square root of 29,929?

Could anyone tell me the square root of 29,929? I can't seem to find it.

little_dragon
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### Re: square root of 29,929?

plug it into a calculator or excel

Motherof8
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### Re: square root of 29,929?

I don't want to use a calculator, I want to figure it out myself. There's another problem I can't seem to solve. THe square root of 67,081. I tried using 809, because 8 squared is 64 and 9 squared is 81, but it didn't work. One book said I could figure out the square root of a number by estimating the root, dividing it into the number, adding it to the quotient, and dividing it by 2 but it didn't work.

little_dragon
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### Re: square root of 29,929?

but 80^2=6400 which is way to small
do numbers that fit better
100^2=10000 is the right number of numbers (5)
200^2=40000 is closer
300^2=90000 is too big
250^2=62500 is better
keep going

for 29929 start closer to 100^2
150^2=22500
keep going

Luke53
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### Re: square root of 29,929?

Could anyone tell me the square root of 29,929? I can't seem to find it.
First make an estimate of what the square root should be: 150^2= 22500, 200^2 =40000 so, the square root must be between 150 and 200.
Let's say it's 150.
29929 / 150 = 199.52 so (199.52 + 150) / 2 = 174.76 doing te same again with the new found number gives: 29929 / 174,76 = 171.25 repeating this with this new found number gives
29929 / 171.25 = 174.76 so (174.76 + 171,25) / 2 = 173.005
The the square root of 29929 must be around 173,(it is 173).
This is what the book says.
Luke

Martingale
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### Re: square root of 29,929?

Could anyone tell me the square root of 29,929? I can't seem to find it.
First make an estimate of what the square root should be: 150^2= 22500, 200^2 =40000 so, the square root must be between 150 and 200.
Let's say it's 150.
29929 / 150 = 199.52 so (199.52 + 150) / 2 = 174.76 doing te same again with the new found number gives: 29929 / 174,76 = 171.25 repeating this with this new found number gives
29929 / 171.25 = 174.76 so (174.76 + 171,25) / 2 = 173.005
The the square root of 29929 must be around 173,(it is 173).
This is what the book says.
Luke
it looks like you are using the bisection method. If you want a quicker method you can try newton's iteration

$x_{n+1}=\frac{x_{n}^2+a}{2x_n}$

where $a$ is the number you want to take the square root of.

for example...
$\begin{array}{c|c} x_n & x_{n+1} \\\hline 100 & 199.645 \\ 199.645 & 174.778 \\ 174.778 & 173.009 \end{array}$

Luke53
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### Re: square root of 29,929?

it looks like you are using the bisection method. If you want a quicker method you can try newton's iteration

Thanks, but I think both methods are pretty useless, only if one still has got a calculator without the "sqrt" function. Doing this without a calculator is not practical, there are simply too many calc's to make. I'd prefer doing this the old fashion way, (if doing it without calculator). Anyway, learned a new method for doing this.
Regards.
Luke.

Martingale
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Location: USA
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### Re: square root of 29,929?

it looks like you are using the bisection method. If you want a quicker method you can try newton's iteration

Thanks, but I think both methods are pretty useless, only if one still has got a calculator without the "sqrt" function. Doing this without a calculator is not practical, there are simply too many calc's to make. I'd prefer doing this the old fashion way, (if doing it without calculator). Anyway, learned a new method for doing this.
Regards.
Luke.

29929 =2 99 29

$1^2<2$

$2a\cdot a\leq199$

$a=7$

$27\cdot 7=189$
$(2\cdot17)a\cdot a\leq 1029$
$34a\cdot a\leq 1029$
$a=3$ since

$343\cdot3=1029$

thus $\sqrt{29929}=173$

Luke53
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### Re: square root of 29,929?

OK!!!

MrAlgebra
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### Re: square root of 29,929?

I don't mean to bump an old thread, but I would start off by realizing that the ones digit of the square root has to be 3 since it ends in 9. Look at the following: 0² = 0, 1² = 1, 2² = 4, 3² = 9, 4² = 16 (ends in 6), 5² = 25 (ends in 5), 6² = 36 (ends in 6), 7² = 49 (ends in 9), 8² = 64 (ends in 4), and 9² = 81 (ends in 1).

Then I would see that the square root has 3 digits because 100² = 10000 and 1000² = 1000000, and 29929 is somewhere in the middle. I'd see that 200² = 40000, so our answer is between 100 and 200. To narrow it down a bit more, we can find that 160² = 25600, we know it's between 160 and 200. There are only a few possibilities to check: 169, 179, 189, 199.

I hope this helps if anyone looks for advice on a similar problem.