9514 1404 393
Answer:
√24 ≈ 4.90
Step-by-step explanation:
The square root can be estimated using a linear interpolation between the perfect squares on either side of the number of interest.
4² = 16
5² = 25
So, √24 can be estimated to be ...
(24 -16)/(25 -16) +4 = 8/9 +4 = 44/9 ≈ 4.8888...
This estimate can be refined by doing one iteration of the Babylonian method. That averages the current guess with the value obtained by dividing 24 by that guess.
√24 ≈ (44/9 +24(9/44))/2 = 4 89/99 ≈ 4.898989...
√24 ≈ 4.90
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A calculator gives the root as approximately 4.89897948557. Rounded to hundredths, that is 4.90.
