By using the table for square root find the value of 13.21 and 21.97
(a) 3.63, 4.60
(b) 3.63, 4.69
(c) 3.53, 4.69
(d) 3.63, 4.19

Question

By using the table for square root find the value of 13.21 and 21.97(a) 3.63, 4.60(b) 3.63, 4.69(c) 3.53, 4.69(d) 3.63, 4.19

Vedantu Content Team · Accepted Answer

Hint: In this question, from the table of square roots we need to check the square root values of the nearest integers and then approximate them according to the given options.

Complete step-by-step answer:

Let us first draw the table of square roots

NUMBER	SQUARE	SQUAREROOT
1	1	1
2	4	1.414
3	9	1.732
4	16	2.000
5	25	2.236
6	36	2.449
7	49	2.646
8	64	2.828
9	81	3.000
10	100	3.162
11	121	3.317
12	144	3.464
13	169	3.606
14	196	3.742
15	225	3.873
16	256	4.000
17	289	4.123
18	324	4.243
19	361	4.359
20	400	4.472
21	441	4.583
22	484	4.690

Now, we need to find the square root of 13.21

As we already know that the number 13.21 lies between the numbers 13 and 14. So, its square root also lies between the square root of 13 and square root of 14.

Now, from the table of square roots we can get that the square root of 13 is 3.606 and similarly the square root of 14 from the table of square roots is 3.742.

Now, the square root of 13.21 lies between 3.606 and 3.742 and we can also say that the square root of 13.21 will be near to 3.606 because 13.21 is near to 13.

Thus, we get from the options that square of 13.21 is 3.63

Now, we need to find the square root of 21.97

As we already know that the number 21.97 lies between the numbers 21 and 22. So, its square root also lies between the square root of 21 and square root of 22.

Now, from the table of square roots we can get that the square root of 21 is 4.583 and similarly the square root of 22 from the table of square roots is 4.690.

Now, the square root of 21.97 lies between 4.583 and 4.690 and we can also say that the square root of 21.97 will be near to 4.690 because 21.97 is near to 22.

Thus, we get from the options that square of 21.97 is 4.69

Hence, the correct option is (b).

Note:
It is important to note that we cannot know the exact value of the square root as the given numbers are not integers. So, the only possible way to calculate their square root is to approximate their values from the known square roots of the integers.
It is also to be noted that after finding the integers between which the given number lies we also need to find which of those two integers is the given number more near to get the precise value of the square root of that number.