find the square root of 5184

Question

phi · Answer

without using a calculator?

if so, find the prime factors.  Start by dividing by 2 as many times as you can.
5184= 2*2592
now divide 2592 by 2 
we get
5184= 2*2*1296

keep going.
then try 3, 5, 7, 13  (the primes) until you end up with all prime factors.
can you do that ?

mrnood · Answer

If no calculator then you could use logs - but you probably need calculator for that (there used to be books with logs in believe it or not!)

If by pencil and paper then use @phi 's method

anonymous · Answer

You can also approximate at first, thinking of square numbers close to 5184, such as $4900=70^2$, then keep moving up the number line.

anonymous · Answer

The number in the one's digit should also give you an indication of what to look for. Which numbers when squared give a 4 in the one's place? 2 and 8 work, so I would guess either 72 or 78.