Question

Find positive square root up to 3 decimal place 1+(0.021)

Answer 1

Answer:

Step 1:

Divide the number (0.1) by 2 to get the first guess for the square root .

First guess = 0.1/2 = 0.05.

Step 2:

Divide 0.1 by the previous result. d = 0.1/0.05 = 2.

Average this value (d) with that of step 1: (2 + 0.05)/2 = 1.025 (new guess).

Error = new guess - previous value = 0.05 - 1.025 = 0.975.

0.975 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 0.1 by the previous result. d = 0.1/1.025 = 0.0975609756.

Average this value (d) with that of step 2: (0.0975609756 + 1.025)/2 = 0.5612804878 (new guess).

Error = new guess - previous value = 1.025 - 0.5612804878 = 0.4637195122.

0.4637195122 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 0.1 by the previous result. d = 0.1/0.5612804878 = 0.1781640413.

Average this value (d) with that of step 3: (0.1781640413 + 0.5612804878)/2 = 0.3697222645 (new guess).

Error = new guess - previous value = 0.5612804878 - 0.3697222645 = 0.1915582233.

0.1915582233 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 0.1 by the previous result. d = 0.1/0.3697222645 = 0.2704732974.

Average this value (d) with that of step 4: (0.2704732974 + 0.3697222645)/2 = 0.3200977809 (new guess).

Error = new guess - previous value = 0.3697222645 - 0.3200977809 = 0.0496244836.

0.0496244836 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 0.1 by the previous result. d = 0.1/0.3200977809 = 0.31240454.

Average this value (d) with that of step 5: (0.31240454 + 0.3200977809)/2 = 0.3162511605 (new guess).

Error = new guess - previous value = 0.3200977809 - 0.3162511605 = 0.0038466204.

0.0038466204 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 0.1 by the previous result. d = 0.1/0.3162511605 = 0.3162043733.

Average this value (d) with that of step 6: (0.3162043733 + 0.3162511605)/2 = 0.3162277669 (new guess).

Error = new guess - previous value = 0.3162511605 - 0.3162277669 = 0.0000233936.

0.0000233936 <= 0.001. As error <= accuracy, we stop the iterations and use 0.3162277669 as the square root