Estimate the square root of 450 to the nearest hundreths place

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 ...

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