Question

find the square root of non perfect square using division method 77. ​

Answer 1

Answer:

The square root of 77 is 8.7749643873921. Or,

The square root of 77 is 8.7749643873921. Or,√77 = 8.7749643871.

Step 1:

Step 1: Divide the number (77) by 2 to get the first guess for the square root .

First guess = 77/2 = 38.5.

Step 2:

Divide 77 by the previous result. d = 77/38.5 = 2.

Average this value (d) with that of step 1: (2 + 38.5)/2 = 20.25 (new guess).

Error = new guess - previous value = 38.5 - 20.25 = 18.25.

18.25 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Step 3: Divide 77 by the previous result. d = 77/20.25 = 3.8024691358.

Average this value (d) with that of step 2: (3.8024691358 + 20.25)/2 = 12.0262345679 (new guess).

Error = new guess - previous value = 20.25 - 12.0262345679 = 8.2237654321.

8.2237654321 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Step 4: Divide 77 by the previous result. d = 77/12.0262345679 = 6.402669062.

Average this value (d) with that of step 3: (6.402669062 + 12.0262345679)/2 = 9.214451815 (new guess).

Error = new guess - previous value = 12.0262345679 - 9.214451815 = 2.8117827529.

2.8117827529 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 77 by the previous result. d = 77/9.214451815 = 8.3564385105.

Average this value (d) with that of step 4: (8.3564385105 + 9.214451815)/2 = 8.7854451628 (new guess).

Error = new guess - previous value = 9.214451815 - 8.7854451628 = 0.4290066522.

0.4290066522 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 77 by the previous result. d = 77/8.7854451628 = 8.7644961152.

Average this value (d) with that of step 5: (8.7644961152 + 8.7854451628)/2 = 8.774970639 (new guess).

Error = new guess - previous value = 8.7854451628 - 8.774970639 = 0.0104745238.

0.0104745238 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Step 7: Divide 77 by the previous result. d = 77/8.774970639 = 8.7749581358.

Average this value (d) with that of step 6: (8.7749581358 + 8.774970639)/2 = 8.7749643874 (new guess).

Error = new guess - previous value = 8.774970639 - 8.7749643874 = 0.0000062516.

0.0000062516 <= 0.001. As error <= accuracy, we stop the iterations and use 8.7749643874 as the square root.

So, we can say that the square root of 77 is 8.77496 with an error smaller than 0.001 (in fact the error is 0.0000062516). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(77)' is 8.774964387392123.