How do you find the square root of 85?

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How do you find the square root of 85?

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Answer 1 · 2015-03-26T03:28:57

$\sqrt{85}$ $sqrt85$ is a non-terminating, non-repeating decimal. You can't finish finding it.
But you can get better and better approximations by: start with a number whose square is close to 85. (9 or 10. $9^{2}$ $9^2$ is closer, so start there.

Now divide 85 by $9$ $9$ to get $9.4444$ $9.4444$ (to 4 places)
Average the two numbers $9$ $9$ and $9.4444$ $9.4444$
$\frac{9 + 9.4444}{2} = 9.2222$ $(9+9.4444)/2=9.2222$

Repeat:
$85 \div 9.2222 = 9.2169$ $85-:9.2222=9.2169$ (rounded to 4 places)
Average: $\frac{9.2222 + 9.2169}{2} = 9.2196$ $(9.2222+9.2169)/2=9.2196$

Repeat:
$85 \div 9.2196 = 9.2195$ $85-:9.2196=9.2195$ (rounded to 4 places)
Average: $\frac{9.2196 + 9.2195}{2} = 9.2196$ $(9.2196+9.2195)/2=9.2196$

$\sqrt{85} \approx 9.2196$ $sqrt85~~9.2196$

That answer is accurate to 4 decimal places. If you need more accuracy, keep more decimal places at each step.

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How do you find the square root of 85?

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