How do you find the square root of 52?

1 Answer
Sep 12, 2015

52=2137.21110

Explanation:

If a,b0 then ab=ab, so:

52=2213=2213=213

If you want to calculate an approximation by hand, you could follow the advice I gave for 28 in http://socratic.org/questions/how-do-you-find-the-square-root-28

Using the method described there:

Let n=52, p0=7, q0=1

Then:

p1=72+5212=49+52=101
q1=271=14

p2=1012+52142=10201+10192=20393
q2=210114=2828

Stopping at this point, we get a result accurate to 5 decimal places:

522039328287.21110