Question

find the sqare root of 62500 with division method and explain this​

Answer 1

Step-by-step explanation:

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Here is the answer to questions like: 62500 square root or what is the square root of 62500?

We must set an error for the final result. Say, smaller than 0.001. In other words we will try to find the square root value with at least 2 correct decimal places.

Step 1:

Divide the number (62500) by 2 to get the first guess for the square root .

First guess = 62500/2 = 31250.

Step 2:

Divide 62500 by the previous result. d = 62500/31250 = 2.

Average this value (d) with that of step 1: (2 + 31250)/2 = 15626 (new guess).

Error = new guess - previous value = 31250 - 15626 = 15624.

15624 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 62500 by the previous result. d = 62500/15626 = 3.9997440164.

Average this value (d) with that of step 2: (3.9997440164 + 15626)/2 = 7814.9998720082 (new guess).

Error = new guess - previous value = 15626 - 7814.9998720082 = 7811.0001279918.

7811.0001279918 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 62500 by the previous result. d = 62500/7814.9998720082 = 7.9974409499.

Average this value (d) with that of step 3: (7.9974409499 + 7814.9998720082)/2 = 3911.4986564791 (new guess).

Error = new guess - previous value = 7814.9998720082 - 3911.4986564791 = 3903.5012155291.

3903.5012155291 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 62500 by the previous result. d = 62500/3911.4986564791 = 15.9785303509.

Average this value (d) with that of step 4: (15.9785303509 + 3911.4986564791)/2 = 1963.738593415 (new guess).

Error = new guess - previous value = 3911.4986564791 - 1963.738593415 = 1947.7600630641.

1947.7600630641 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 62500 by the previous result. d = 62500/1963.738593415 = 31.8270467411.

Average this value (d) with that of step 5: (31.8270467411 + 1963.738593415)/2 = 997.7828200781 (new guess).

Error = new guess - previous value = 1963.738593415 - 997.7828200781 = 965.9557733369.

965.9557733369 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 62500 by the previous result. d = 62500/997.7828200781 = 62.6388816708.

Average this value (d) with that of step 6: (62.6388816708 + 997.7828200781)/2 = 530.2108508745 (new guess).

Error = new guess - previous value = 997.7828200781 - 530.2108508745 = 467.5719692036.

467.5719692036 > 0.001. As error > accuracy, we repeat this step again.

Step 8:

Divide 62500 by the previous result. d = 62500/530.2108508745 = 117.8776328265.

Average this value (d) with that of step 7: (117.8776328265 + 530.2108508745)/2 = 324.0442418505 (new guess).

Error = new guess - previous value = 530.2108508745 - 324.0442418505 = 206.166609024.

206.166609024 > 0.001. As error > accuracy, we repeat this step again.

Step 9:

Divide 62500 by the previous result. d = 62500/324.0442418505 = 192.8748977087.

Average this value (d) with that of step 8: (192.8748977087 + 324.0442418505)/2 = 258.4595697796 (new guess).

Error = new guess - previous value = 324.0442418505 - 258.4595697796 = 65.5846720709.

65.5846720709 > 0.001. As error > accuracy, we repeat this step again.

Step 10:

Divide 62500 by the previous result. d = 62500/258.4595697796 = 241.8173180947.

Average this value (d) with that of step 9: (241.8173180947 + 258.4595697796)/2 = 250.1384439372 (new guess).

Error = new guess - previous value = 258.4595697796 - 250.1384439372 = 8.3211258424.

8.3211258424 > 0.001. As error > accuracy, we repeat this step again.

Step 11:

Divide 62500 by the previous result. d = 62500/250.1384439372 = 249.8616326873.

Average this value (d) with that of step 10: (249.8616326873 + 250.1384439372)/2 = 250.0000383123 (new guess).

Error = new guess - previous value = 250.1384439372 - 250.0000383123 = 0.1384056249.

0.1384056249 > 0.001. As error > accuracy, we repeat this step again.

Step 12:

Divide 62500 by the previous result. d = 62500/250.0000383123 = 249.9999616877.

Average this value (d) with that of step 11: (249.9999616877 + 250.0000383123)/2 = 250 (new guess).

Error = new guess - previous value = 250.0000383123 - 250 = 0.0000383123.

0.0000383123 <= 0.001. As error <= accuracy, we stop the iterations and use 250 as the square root.

So, we can say that the square root of 62500 is 250 with an error smaller than 0.001 (in fact the error is 0.0000383123). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function (62500) is 250.

Note: There are other ways to calculate square roots. This is only one of them.