We can round it off to four decimal places, i.e. 3.4651.
3.31662
and evaluate each of the following:
(i)
Given: √3 = 1.732
(ii) 28.867
(i)
(ii)
(iii)
(iv)
(v)
=1.732×2.236=3.873
=1.414×6.083
=8.602
=1.414×6.403
=9.055
=1.414×3×3.317
= 14.070
=2×3×1.732×2.2361
=23.24
=1.7321×5.385×10
=93.27
=11×5.3851
=59.235
=13 ×6.4031
=83.239
=1.732 ×5×7×2.646
=160.41
=2×2×1.414×6.4031
=36.222
The square root of 131 is not listed in the table. Hence, we have to apply long division to find it.
Substituting the values:
= 2×2×11.4455 (using the table to find √2)
= 64.75
The square root of 991 is not listed in the table; it lists the square roots of all the numbers below 100.
Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner:
Now, we have to find the square root of 49.55.
We have:
Their difference is 0.071.
Thus, for the difference of 1 (50 − 49), the difference in the values of the square roots is 0.071.
For the difference of 0.55, the difference in the values of the square roots is:
0.55 × 0.0701 = 0.03905
7+0.03905=7.03905
Finally, we have:
×10=7.03905×10=70.3905
(using the square root table to find √11)
=0.829
(using the square root table to find
0.581
The square root of 101 is not listed in the table. This is because the table lists the square roots of all the numbers below 100.
Hence, we have to manipulate the number such that we get the square root of a number less than 100. This can be done in the following manner:
Now, we have to find the square root of 1.01.
We have:
Their difference is 0.414.
Thus, for the difference of 1 (2 − 1), the difference in the values of the square roots is 0.414.
For the difference of 0.01, the difference in the values of the square roots is:
0.01 × 0.414 = 0.00414
∴ 1+0.00414=1.00414
×10=1.00414×10=10.0414Their difference is 0.136.
Thus, for the difference of 1 (14 − 13), the difference in the values of the square roots is 0.136.
For the difference of 0.21, the difference in the values of their square roots is:
0.136×0.21=0.02856
From the square root table, we have:
Their difference is 0.107.
Thus, for the difference of 1 (22 − 21), the difference in the values of the square roots is 0.107.
For the difference of 0.97, the difference in the values of their square roots is:
0.107×0.97=0.104
4.583+0.104≈4.687
=1.414×2.236×3.317 (Using the square root table to find all the square roots)
=10.488
=1.414×1.732×2.236×6.083 (Using the table to find all the square roots )=33.312
Their difference is 0.1474.
Thus, for the difference of 1 (12 − 11), the difference in the values of the square roots is 0.1474.
For the difference of 0.11, the difference in the values of the square roots is:
0.11 × 0.1474 = 0.0162
3.3166+0.0162=3.328≈3.333
=5×3.605
=18.030
Hence, the length of one side of the field is 18.030 m.
∴
=2×2×5
=129.60 m
Hence, the length of one side of the square is 129.60 m
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