Find the square root of 761 by by division method
Answers
Answer:
27.5
Step-by-step explanation:
Step 1)
Set up 761 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
7 61 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 7 is 4, and the square root of 4 is 2. Therefore, put 2 on top and 4 at the bottom like this:
2
7 61 00
4
Step 3)
Calculate 7 minus 4 and put the difference below. Then move down the next set of numbers.
2
7 61 00
4
3 61
Step 4)
Double the number in green on top: 2 × 2 = 4. Then, use 4 and the bottom number to make this problem:
4? × ? ≤ 361
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 7. Replace the question marks in the problem with 7 to get:
47 × 7 = 329.
Now, enter 7 on top, and 329 at the bottom:
2 7
7 61 00
4
3 61
3 29
Step 5)
Calculate 361 minus 329 and put the difference below. Then move down the next set of numbers.
2 7
7 61 00
4
3 61
3 29
0 32 00
Step 6)
Double the number in green on top: 27 × 2 = 54. Then, use 54 and the bottom number to make this problem:
54? × ? ≤ 3200
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 5. Now, enter 5 on top:
2 7 5
7 61 00
4
3 61
3 29
0 32 00
That's it! The answer is on top. The square root of 761 with one digit decimal accuracy is 27.5. Did you notice that the last two steps repeat the previous two steps. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.
Answer:
27.586228448267445
Step-by-step explanation:
Step 1:
Divide the number (761) by 2 to get the first guess for the square root .
First guess = 761/2 = 380.5.
Step 2:
Divide 761 by the previous result. d = 761/380.5 = 2.
Average this value (d) with that of step 1: (2 + 380.5)/2 = 191.25 (new guess).
Error = new guess - previous value = 380.5 - 191.25 = 189.25.
189.25 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 761 by the previous result. d = 761/191.25 = 3.9790849673.
Average this value (d) with that of step 2: (3.9790849673 + 191.25)/2 = 97.6145424837 (new guess).
Error = new guess - previous value = 191.25 - 97.6145424837 = 93.6354575163.
93.6354575163 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 761 by the previous result. d = 761/97.6145424837 = 7.7959695414.
Average this value (d) with that of step 3: (7.7959695414 + 97.6145424837)/2 = 52.7052560126 (new guess).
Error = new guess - previous value = 97.6145424837 - 52.7052560126 = 44.9092864711.
44.9092864711 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 761 by the previous result. d = 761/52.7052560126 = 14.4387876575.
Average this value (d) with that of step 4: (14.4387876575 + 52.7052560126)/2 = 33.5720218351 (new guess).
Error = new guess - previous value = 52.7052560126 - 33.5720218351 = 19.1332341775.
19.1332341775 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 761 by the previous result. d = 761/33.5720218351 = 22.6676845302.
Average this value (d) with that of step 5: (22.6676845302 + 33.5720218351)/2 = 28.1198531827 (new guess).
Error = new guess - previous value = 33.5720218351 - 28.1198531827 = 5.4521686524.
5.4521686524 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 761 by the previous result. d = 761/28.1198531827 = 27.0627302019.
Average this value (d) with that of step 6: (27.0627302019 + 28.1198531827)/2 = 27.5912916923 (new guess).
Error = new guess - previous value = 28.1198531827 - 27.5912916923 = 0.5285614904.
0.5285614904 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 761 by the previous result. d = 761/27.5912916923 = 27.5811661334.
Average this value (d) with that of step 7: (27.5811661334 + 27.5912916923)/2 = 27.5862289129 (new guess).
Error = new guess - previous value = 27.5912916923 - 27.5862289129 = 0.0050627794.
0.0050627794 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 761 by the previous result. d = 761/27.5862289129 = 27.5862279836.
Average this value (d) with that of step 8: (27.5862279836 + 27.5862289129)/2 = 27.5862284483 (new guess).
Error = new guess - previous value = 27.5862289129 - 27.5862284483 = 4.646e-7.
4.646e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 27.5862284483 as the square root.
So, we can say that the square root of 761 is 27.586228 with an error smaller than 0.001 (in fact the error is 4.646e-7). this means that the first 6 decimal places are correct. Just to compare, the returned value by using the javascript function (761)' is 27.586228448267445.