SOLUTION: how shall i find the square root of 289 without using calculator?

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Question 1018059: how shall i find the square root of 289
without using calculator?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What squares do you know or can you find near 289?

system%2820%5E2=400%2C14%5E2=196%2C15%5E2=3%5E3%2A5%5E2=9%2A25=225%29

Look at squares between 15%5E2 and 20%5E2.
Maybe try %28x%2B15%29%28x%2B15%29=289
x%5E2%2B30x%2B225=289
x%5E2%2B30x%2B225-289=0
x%5E2%2B30x-64=0
One factorization of 64 is 16%2A4 and another is 32%2A2. This last one looks like it can work.

x%5E2%2B30x-64=%28x-2%29%28x%2B32%29=0
Either x=2 OR x=-32.

The number can be x%2B2=15%2B2=17.
Try checking the square of 17...
highlight%2817%2A17=289%29.

x=-32 may also work.
15-32=-17 and you easily find %28-17%29%2A%28-17%29=%281%29%2A17%5E2=289.

highlight%28sqrt%28289%29=0%2B-+17%29.