Find the square root of 707
Answers
26.5894716006 this is your answer
Answer:
26.589471600616662.
Step-by-step explanation: Step 1:
Divide the number (707) by 2 to get the first guess for the square root .
First guess = 707/2 = 353.5.
Step 2:
Divide 707 by the previous result. d = 707/353.5 = 2.
Average this value (d) with that of step 1: (2 + 353.5)/2 = 177.75 (new guess).
Error = new guess - previous value = 353.5 - 177.75 = 175.75.
175.75 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 707 by the previous result. d = 707/177.75 = 3.9774964838.
Average this value (d) with that of step 2: (3.9774964838 + 177.75)/2 = 90.8637482419 (new guess).
Error = new guess - previous value = 177.75 - 90.8637482419 = 86.8862517581.
86.8862517581 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 707 by the previous result. d = 707/90.8637482419 = 7.7808808648.
Average this value (d) with that of step 3: (7.7808808648 + 90.8637482419)/2 = 49.3223145534 (new guess).
Error = new guess - previous value = 90.8637482419 - 49.3223145534 = 41.5414336885.
41.5414336885 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 707 by the previous result. d = 707/49.3223145534 = 14.3342826954.
Average this value (d) with that of step 4: (14.3342826954 + 49.3223145534)/2 = 31.8282986244 (new guess).
Error = new guess - previous value = 49.3223145534 - 31.8282986244 = 17.494015929.
17.494015929 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 707 by the previous result. d = 707/31.8282986244 = 22.2129372463.
Average this value (d) with that of step 5: (22.2129372463 + 31.8282986244)/2 = 27.0206179354 (new guess).
Error = new guess - previous value = 31.8282986244 - 27.0206179354 = 4.807680689.
4.807680689 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 707 by the previous result. d = 707/27.0206179354 = 26.1652047222.
Average this value (d) with that of step 6: (26.1652047222 + 27.0206179354)/2 = 26.5929113288 (new guess).
= new guess - previous value = 27.0206179354 - 26.5929113288 = 0.4277066066.
0.4277066066 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 707 by the previous result. d = 707/26.5929113288 = 26.5860323174.
Average this value (d) with that of step 7: (26.5860323174 + 26.5929113288)/2 = 26.5894718231 (new guess).
Error = new guess - previous value = 26.5929113288 - 26.5894718231 = 0.0034395057.
0.0034395057 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 707 by the previous result. d = 707/26.5894718231 = 26.5894713781.
Average this value (d) with that of step 8: (26.5894713781 + 26.5894718231)/2 = 26.5894716006 (new guess).
Error = new guess - previous value = 26.5894718231 - 26.5894716006 = 2.225e-7.
2.225e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 26.5894716006 as the square root.
So, we can say that the square root of 707 is 26.589471 with an error smaller than 0.001 (in fact the error is 2.225e-7). this means that the first 6 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(707)' is 26.589471600616662.
Note: There are other ways to calculate square roots. This is only one of them.
What is square root?
Definition of square root
A square root of a number 'a' is a number x such that x2 = a, in other words, a number x whose square is a. For example, 26 is the square root of 676 because 262 = 26•26 = 676, -26 is square root of 676 because (-26)2 = (-26)•(-26) = 676.