Question

How to find Square root of
1)676
2)674
With best explanation
I'll mark u brainliest

Answer 1

dear your answer is
1 676 =26
2 674 =25.96 .......
thanks

Answer 2

hey friend,
here is your answer
1- square root of 676
firstly find the LCM OF 676,
WE GET, 2*2*13*13
NOW WE FIND PAIRS= 1PAIR OF 2 AND 1 OF 13 IS THERE, SO 2*13=26 IS THE square root.
2- 674=
again by the same process,
LCM of 674=Step 1: 
 Divide the number (674) by 2 to get the first guess for the square root .
 First guess = 674/2 = 337.Step 2:
 Divide 674 by the previous result. d = 674/337 = 2.
 Average this value (d) with that of step 1: (2 + 337)/2 = 169.5 (new guess).
 Error = new guess - previous value = 337 - 169.5 = 167.5.
 167.5 > 0.001. As error > accuracy, we repeat this step again.Step 3:
 Divide 674 by the previous result. d = 674/169.5 = 3.9764011799.
 Average this value (d) with that of step 2: (3.9764011799 + 169.5)/2 = 86.73820059(new guess).
 Error = new guess - previous value = 169.5 - 86.73820059 = 82.76179941.
 82.76179941 > 0.001. As error > accuracy, we repeat this step again.Step 4:
 Divide 674 by the previous result. d = 674/86.73820059 = 7.7705093651.
 Average this value (d) with that of step 3: (7.7705093651 + 86.73820059)/2 = 47.2543549776 (new guess).
 Error = new guess - previous value = 86.73820059 - 47.2543549776 = 39.4838456124.
 39.4838456124 > 0.001. As error > accuracy, we repeat this step again.Step 5:
 Divide 674 by the previous result. d = 674/47.2543549776 = 14.2632356387.
 Average this value (d) with that of step 4: (14.2632356387 + 47.2543549776)/2 = 30.7587953082 (new guess).
 Error = new guess - previous value = 47.2543549776 - 30.7587953082 = 16.4955596694.
 16.4955596694 > 0.001. As error > accuracy, we repeat this step again.Step 6:
 Divide 674 by the previous result. d = 674/30.7587953082 = 21.9124316556.
 Average this value (d) with that of step 5: (21.9124316556 + 30.7587953082)/2 = 26.3356134819 (new guess).
 Error = new guess - previous value = 30.7587953082 - 26.3356134819 = 4.4231818263.
 4.4231818263 > 0.001. As error > accuracy, we repeat this step again.Step 7:
 Divide 674 by the previous result. d = 674/26.3356134819 = 25.5927206884.
 Average this value (d) with that of step 6: (25.5927206884 + 26.3356134819)/2 = 25.9641670852 (new guess).
 Error = new guess - previous value = 26.3356134819 - 25.9641670852 = 0.3714463967.
 0.3714463967 > 0.001. As error > accuracy, we repeat this step again.Step 8:
 Divide 674 by the previous result. d = 674/25.9641670852 = 25.9588531297.
 Average this value (d) with that of step 7: (25.9588531297 + 25.9641670852)/2 = 25.9615101075 (new guess).
 Error = new guess - previous value = 25.9641670852 - 25.9615101075 = 0.0026569777.
 0.0026569777 > 0.001. As error > accuracy, we repeat this step again.Step 9:
 Divide 674 by the previous result. d = 674/25.9615101075 = 25.9615098355.
 Average this value (d) with that of step 8: (25.9615098355 + 25.9615101075)/2 = 25.9615099715 (new guess).
 Error = new guess - previous value = 25.9615101075 - 25.9615099715 = 1.36e-7.
 1.36e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 25.9615099715 as the square root.

So, we can say that the square root of 674 is 25.961509 with an error smaller than 0.001 (in fact the error is 1.36e-7). this means that the first 6 decimal places are correct. Just to compare, the returned value by using the function (674)' is 25.96150997149434.

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