Use the babylonian method to approximate square root of 24 to the nearest hundredth.

1 answer:

6 0

We will start with our guess of 12, since 12*2 = 24.
Divide 24 by 12; 24/12=2. Average this answer with our guess: (12+2)/2=7. This is our new guess.
24/7=3.428571429. Average this with our guess of 7: (3.428571429+7)/2=5.214285715. This is our new guess.
24/5.214285715=4.602739726. Averaging with our guess: (4.602739726+5.214285715)/2=4.90851272. New guess!
24/4.90851272=4.889464766. Averaging with our guess: (4.889464766+4.90851272)/2=4.898988743. New guess! You can see as we go through our guesses are closer and closer to the same number...)
24/4.898988743=4.898970228. Averaging: (4.898970228+4.898988743)/2=4.898979486. At this point our answer is the same every time down to the hundred-thousandth. Our estimate to the nearest hundredth would be 4.90.

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