Estimate the square root of 450 to the nearest hundreths place

The square root of 450 is 21. 2132034356 but when simplified to the nearest hundredth it is 21.213

Assume all in the head, no calculators.

450 is close to 21^2=441, so our initial estimate x0=21

a better estimate, using Newton's method,

x1=x0 - (x0^2-450) / (2*x0)

=21 - (21^2-450) / (2*21)

=21+9/42=21+3/14=21+1.5/7 [1.5/7 is easier in the head is easier to do than 9/42]

=21+0.21428 ...

=21.21 (to two places)

Exact value is 21.2132034 ...