Exercise 3.9
Using square root table, find the square roots of the following:
1.) 7
Solution:
From the table, we directly find that square root of is 2.646
2.) 15
Solution:
3.) 74
Solution:
4.) 82
Solution:
5.) 198
Solution:
6.) 540
Solution:
7.) 8700
Solution:
8.) 3509
Solution:
9.) 6929
Solution:
10.) 25725
Solution:
11.) 1312
Solution:
12.) 4192
Solution:
13.) 4955
Solution:
On prime factorization:
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
Their difference is 0.071 Thus, for the difference of 1 (50-49), the difference in the values of square roots is 0,071
For the difference of 0.55, the difference in the values of the square roots is:
0.55 x 0.0701 = 0.03905
Finally, we have:
Solution:
he square 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 .414.
Thus, for the difference of 1(2 -1 ), the difference in the values of the square roots is .414.
For the difference of .01, the difference in the values of the square roots is:
0.1 x 0.414 = 0.00414
This value is really close of the one from the key answer.
17.) 13.21
Solution:
From the square root, we have:
Their 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 x 0.21 = 0.2856
18.) 21.97
Solution:
20.) 1110
Solution:
= 1.414 x 1.732 x 2.236 x 6.083 (using the table to find all the square roots) = 33.312
21.) 11.11
Solution:
We have:
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:
22.) The area of a square field is 325 m2. Find the appropriate length of one side of the field.
Solution:
The length of one side of the square field will be the square root of 325.
= 5 x 3.605
Hence, the length of one side of the field is 18.030 m.
23.) Find the length of a side of a square, whose area is equal to the area of a rectangle with sides 240 m and 70 m.
Solution:
The area of the rectangle = 240 m x 70 m = 16800 m2
Given that the length of the square is equal to the area of the rectangle.
Hence, the area of the square will also be 16800 m2.
The length of one side of a square is the square root of its area.
Hence, the length of one side of the square is 129.60 m.