Table of Square Roots

x \sqrt{x} x \sqrt{x} x \sqrt{x} x \sqrt{x} x \sqrt{x}
1 1.000 21 4.583 41 6.403 61 7.810 81 9.000
2 1.414 22 4.690 42 6.481 62 7.874 82 9.055
3 1.732 23 4.796 43 6.557 63 7.937 83 9.110
4 2.000 24 4.899 44 6.633 64 8.000 84 9.165
5 2.236 25 5.000 45 6.708 65 8.062 85 9.220
6 2.449 26 5.099 46 6.782 66 8.124 86 9.274
7 2.646 27 5.196 47 6.856 67 8.185 87 9.327
8 2.828 28 5.292 48 6.928 68 8.246 88 9.381
9 3.000 29 5.385 49 7.000 69 8.307 89 9.434
10 3.162 30 5.477 50 7.071 70 8.367 90 9.487
11 3.317 31 5.568 51 7.141 71 8.426 91 9.539
12 3.464 32 5.657 52 7.211 72 8.485 92 9.592
13 3.606 33 5.745 53 7.280 73 8.544 93 9.644
14 3.742 34 5.831 54 7.348 74 8.602 94 9.695
15 3.873 35 5.916 55 7.416 75 8.660 95 9.747
16 4.000 36 6.000 56 7.483 76 8.718 96 9.798
17 4.123 37 6.083 57 7.550 77 8.775 97 9.849
18 4.243 38 6.164 58 7.616 78 8.832 98 9.899
19 4.359 39 6.245 59 7.681 79 8.888 99 9.950
20 4.472 40 6.325 60 7.746 80 8.944 100 10.000

Question: Using the square root table, please find the values of the following:

1. \sqrt{(8 )}      2. \sqrt{29}      3. \sqrt{73}      4. \sqrt{124}      5. \sqrt{148}      6. \sqrt{212}

7. \sqrt{549}      8. \sqrt{2075}      9. \sqrt{3312}      10. \sqrt{3000}      11. \sqrt{\frac{7}{81}}      12. \sqrt{\frac{99}{144}}

Answer:

1. \sqrt{(8 )}=2.828

2. \sqrt{29}=5.385

3. \sqrt{73}=8.544

4. \sqrt{124}= \sqrt{(2 \times 2 \times 31)}=2\sqrt{31}=2 \times 5.568=11.136

5. \sqrt{148}= \sqrt{(2 \times 2 \times 37)}=3\sqrt{37}=2 \times 6.083=12.166

6. \sqrt{212}= \sqrt{(2 \times 2 \times 53)}=2\sqrt{53}=2 \times 7.280=14.56

7. \sqrt{549}= \sqrt{(3 \times 3 \times 61)}=3\sqrt{61}=3 \times 7.810=23.43

8. \sqrt{2075}= \sqrt{(5 \times 5 \times 83)}=5\sqrt{83}=5 \times 9.110=45.55

9. \sqrt{3312}= \sqrt{4 \times 4 \times 3 \times 3 \times 23}=4 \times 3 \times \sqrt{23} =12 \times 4.796=57.552

10. \sqrt{3000}=10\sqrt{30}=10 \times 5.477=54.77

11. \sqrt{\frac{7}{81}} = \frac{\sqrt{7}}{\sqrt{81}} = \frac{\sqrt{7}}{9} = \frac{2.646}{9} =0.294

12. \sqrt{\frac{99}{144}} = \frac{3\sqrt{33}}{12} = \frac{3 \times 5.745}{12} =1.43625