Question

find the square root of 4225 by long division method

Answer 1

Here is your answer.

Hope it will be helpful for you.

Answer 2

Answer:

here's the long methord

Step-by-step explanation:

Step 1:

Divide the number (4225) by 2 to get the first guess for the square root .

First guess = 4225/2 = 2112.5.

Step 2:

Divide 4225 by the previous result. d = 4225/2112.5 = 2.

Average this value (d) with that of step 1: (2 + 2112.5)/2 = 1057.25 (new guess).

Error = new guess - previous value = 2112.5 - 1057.25 = 1055.25.

1055.25 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 4225 by the previous result. d = 4225/1057.25 = 3.9962165997.

Average this value (d) with that of step 2: (3.9962165997 + 1057.25)/2 = 530.6231082998 (new guess).

Error = new guess - previous value = 1057.25 - 530.6231082998 = 526.6268917002.

526.6268917002 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 4225 by the previous result. d = 4225/530.6231082998 = 7.9623369844.

Average this value (d) with that of step 3: (7.9623369844 + 530.6231082998)/2 = 269.2927226421 (new guess).

Error = new guess - previous value = 530.6231082998 - 269.2927226421 = 261.3303856577.

261.3303856577 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 4225 by the previous result. d = 4225/269.2927226421 = 15.6892468484.

Average this value (d) with that of step 4: (15.6892468484 + 269.2927226421)/2 = 142.4909847453 (new guess).

Error = new guess - previous value = 269.2927226421 - 142.4909847453 = 126.8017378968.

126.8017378968 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 4225 by the previous result. d = 4225/142.4909847453 = 29.6509986758.

Average this value (d) with that of step 5: (29.6509986758 + 142.4909847453)/2 = 86.0709917106 (new guess).

Error = new guess - previous value = 142.4909847453 - 86.0709917106 = 56.4199930347.

56.4199930347 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 4225 by the previous result. d = 4225/86.0709917106 = 49.0873860755.

Average this value (d) with that of step 6: (49.0873860755 + 86.0709917106)/2 = 67.5791888931 (new guess).

Error = new guess - previous value = 86.0709917106 - 67.5791888931 = 18.4918028175.

18.4918028175 > 0.001. As error > accuracy, we repeat this step again.

Step 8:

Divide 4225 by the previous result. d = 4225/67.5791888931 = 62.5192469635.

Average this value (d) with that of step 7: (62.5192469635 + 67.5791888931)/2 = 65.0492179283 (new guess).

Error = new guess - previous value = 67.5791888931 - 65.0492179283 = 2.5299709648.

2.5299709648 > 0.001. As error > accuracy, we repeat this step again.

Step 9:

Divide 4225 by the previous result. d = 4225/65.0492179283 = 64.9508193113.

Average this value (d) with that of step 8: (64.9508193113 + 65.0492179283)/2 = 65.0000186198 (new guess).

Error = new guess - previous value = 65.0492179283 - 65.0000186198 = 0.0491993085.

0.0491993085 > 0.001. As error > accuracy, we repeat this step again.

Step 10:

Divide 4225 by the previous result. d = 4225/65.0000186198 = 64.9999813802.

Average this value (d) with that of step 9: (64.9999813802 + 65.0000186198)/2 = 65 (new guess).

Error = new guess - previous value = 65.0000186198 - 65 = 0.0000186198.

0.0000186198 <= 0.001. As error <= accuracy, we stop the iterations and use 65 as the square root.