Question

solution of square root of 24.75

Answer 1

Answer:

Step 1:

Divide the number (24.75) by 2 to get the first guess for the square root .

First guess = 24.75/2 = 12.375.

Step 2:

Divide 24.75 by the previous result. d = 24.75/12.375 = 2.

Average this value (d) with that of step 1: (2 + 12.375)/2 = 7.1875 (new guess).

Error = new guess - previous value = 12.375 - 7.1875 = 5.1875.

5.1875 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 24.75 by the previous result. d = 24.75/7.1875 = 3.4434782609.

Average this value (d) with that of step 2: (3.4434782609 + 7.1875)/2 = 5.3154891305 (new guess).

Error = new guess - previous value = 7.1875 - 5.3154891305 = 1.8720108695.

1.8720108695 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 24.75 by the previous result. d = 24.75/5.3154891305 = 4.6562036705.

Average this value (d) with that of step 3: (4.6562036705 + 5.3154891305)/2 = 4.9858464005 (new guess).

Error = new guess - previous value = 5.3154891305 - 4.9858464005 = 0.32964273.

0.32964273 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 24.75 by the previous result. d = 24.75/4.9858464005 = 4.9640518403.

Average this value (d) with that of step 4: (4.9640518403 + 4.9858464005)/2 = 4.9749491204 (new guess).

Error = new guess - previous value = 4.9858464005 - 4.9749491204 = 0.0108972801.

0.0108972801 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 24.75 by the previous result. d = 24.75/4.9749491204 = 4.9749252507.

Average this value (d) with that of step 5: (4.9749252507 + 4.9749491204)/2 = 4.9749371856 (new guess).

Error = new guess - previous value = 4.9749491204 - 4.9749371856 = 0.0000119348.

0.0000119348 <= 0.001. As error <= accuracy, we stop the iterations and use 4.9749371856 as the square root

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