what is the way to find the square root of 3600.720036 witout using calculator?

Answer 1

Because you see the pattern of 36 - 72 - 36 in the digits, it should look like the 1-2-1 pattern in x^2 + 2xy + y^2, which is (x+y)^2.

If you can figure out what x and y are, then the square root of (x+y)^2 is just (x+y).

Think of 3600 as x^2 (x=60), and 0.000036 as y^2 (y=0.006)... you can do both of those in your head, easily. Then verify that 2xy = 0.72, the remainder not yet accounted for, which it does.

The square root of that expression is just (x+y) = 60.006

Answer 2

you can give an appoximate number... since you know that the sqr of 36 is 6.

so the sqr will be a little more than 60... actually 60.00X

Answer 3

(60+e)^2 = 3600.720036
e^2 + 120e = 0.720036
so e ~ 0.72/120 = 0.006
60.006^2 = 3600.72036
so we have exact answer and no further approx needed.