Question

square root of 10,000 Sept by sept explanation​

Answer 1

Step 1:

Divide the number (10000) by 2 to get the first guess for the square root .

First guess = 10000/2 = 5000.

Step 2:

Divide 10000 by the previous result. d = 10000/5000 = 2.

Average this value (d) with that of step 1: (2 + 5000)/2 = 2501 (new guess).

Error = new guess - previous value = 5000 - 2501 = 2499.

2499 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 10000 by the previous result. d = 10000/2501 = 3.9984006397.

Average this value (d) with that of step 2: (3.9984006397 + 2501)/2 = 1252.4992003199 (new guess).

Error = new guess - previous value = 2501 - 1252.4992003199 = 1248.5007996801.

1248.5007996801 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 10000 by the previous result. d = 10000/1252.4992003199 = 7.9840370337.

Average this value (d) with that of step 3: (7.9840370337 + 1252.4992003199)/2 = 630.2416186768 (new guess).

Error = new guess - previous value = 1252.4992003199 - 630.2416186768 = 622.2575816431.

622.2575816431 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 10000 by the previous result. d = 10000/630.2416186768 = 15.8669305607.

Average this value (d) with that of step 4: (15.8669305607 + 630.2416186768)/2 = 323.0542746188 (new guess).

Error = new guess - previous value = 630.2416186768 - 323.0542746188 = 307.187344058.

307.187344058 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 10000 by the previous result. d = 10000/323.0542746188 = 30.9545509398.

Average this value (d) with that of step 5: (30.9545509398 + 323.0542746188)/2 = 177.0044127793 (new guess).

Error = new guess - previous value = 323.0542746188 - 177.0044127793 = 146.0498618395.

146.0498618395 > 0.001. As error > accuracy, we repeat this step again

Step 7:

Divide 10000 by the previous result. d = 10000/177.0044127793 = 56.4957666477.

Average this value (d) with that of step 6: (56.4957666477 + 177.0044127793)/2 = 116.7500897135 (new guess).

Error = new guess - previous value = 177.0044127793 - 116.7500897135 = 60.2543230658.

60.2543230658 > 0.001. As error > accuracy, we repeat this step again.

Step 8:

Divide 10000 by the previous result. d = 10000/116.7500897135 = 85.6530391072.

Average this value (d) with that of step 7: (85.6530391072 + 116.7500897135)/2 = 101.2015644104 (new guess).

Error = new guess - previous value = 116.7500897135 - 101.2015644104 = 15.5485253031.

15.5485253031 > 0.001. As error > accuracy, we repeat this step again.

Step 9:

Divide 10000 by the previous result. d = 10000/101.2015644104 = 98.8127017429.

Average this value (d) with that of step 8: (98.8127017429 + 101.2015644104)/2 = 100.0071330767 (new guess).

Error = new guess - previous value = 101.2015644104 - 100.0071330767 = 1.1944313337.

1.1944313337 > 0.001. As error > accuracy, we repeat this step again.

Step 10:

Divide 10000 by the previous result. d = 10000/100.0071330767 = 99.9928674321.

Average this value (d) with that of step 9: (99.9928674321 + 100.0071330767)/2 = 100.0000002544 (new guess).

Error = new guess - previous value = 100.0071330767 - 100.0000002544 = 0.0071328223.

0.0071328223 > 0.001. As error > accuracy, we repeat this step again.

Step 11:

Divide 10000 by the previous result. d = 10000/100.0000002544 = 99.9999997456.

Average this value (d) with that of step 10: (99.9999997456 + 100.0000002544)/2 = 100 (new guess).

Error = new guess - previous value = 100.0000002544 - 100 = 2.544e-7.

2.544e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 100 as the square root

Answer 2

Step-by-step explanation:

$\sqrt{10000} = \sqrt{100 \times 100} \\ \sqrt{100} = 10 \\ so \: \sqrt{100} \times \sqrt{100} = 10 \times 10 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 \\ \sqrt{10000} = 100$