## Question: Using the square root table find the square roots of the following

Note:You may access the table of squares and square roots here.

### (1) 7

**Solution:**

We know that 7 is a prime number.

So from the square root table, the square root of 7 is 2.646

### (2) 15

**Solution:**

Here we can write 15 as 3*5

Now we have to find the square root of 3 and 5.

Here the square root of 3 is 1.732 and 5 is 2.236

So the square root of 15 = square root of 3 * square root of 5

= (1.732) * (2.236)

= 3.873

### (3) 74

**Solution:**

Here we can write 74 as 2 * 37

Here the square root of 2 is 1.414 and the square root of 37 is 6.083

So the square root of 74 = square root of 2 * square root of 37

= (1.414) * (6.083)

= 8.602

### (4) 82

**Solution:**

Here we can write 82 as 2 * 41

Now we have to find the square root of 2 and 41

Here the square root of 2 is 1.414 and the square root of 41 is 6.483

So the square root of 82 = square root of 2 * square root of 41

= (1.414) * (6.483)

= 9.055

### (5) 198

**Solution:**

Here we can write 198 as 2 * 9 * 11

We know that the square root of 2 is 1.414 and 9 is 3

From the square root table, the square root of 11 is 3.3166

So the square root of 198 = square root of 2 * square root of 11 * square root of 9

= (1.414) * (3.3166) * (3)

= 14.069

### (6) 540

**Solution:**

Here we can write 540 as 3 * 4 * 9 * 5

So we know the square root of 3 is 1.73 and 4 is 2 and 9 is 3 and 5 is 2.236

So the square root of 540 = (1.73) * (2) * (3) * (2.236)

= 23.21

### (7) 8700

**Solution:**

Here we can write 8700 as 3 * 29 * 100

We know the square root of 3 is 1.73 and 100 is 10

The square root of 29 is 5.385

So the square root of 8700 = (1.73) * (5.385) * (10)

= 93.16

### (8) 3509

**Solution:**

Here we can write 3509 as 29 * 121

The square root of 29 is 5.385 and 121 is 11

So the square root of 8700 = (5.385) * (11)

= 59.23

### (9) 6929

**Solution:**

Here we can write 6929 as 169 * 41

We know that the square root of 169 is 13

The square root of 41 is 6.403

So the square root of 6929 = (13) * (6.403)

= 83.24

### (10) 25725

**Solution:**

Hear we can write 25725 as 3 * 7 * 25 * 49

We know that the square root of 3 is 1.732 and 7 is 2.645 and 25 is 5 and 49 is 7

So the square root of 25725 = (1.372) * (2.645) * (5) * (7)

= 160.41

### (11) 1312

**Solution:**

Here we can write 1312 as 2 * 16 * 41

We know that the square root of 2 is 1.414 and 16 is 4

Here the square root of 41 is 6.403

So the square root of 1312 = (1.414) * (4) * (6.403)

= 36.22

### (12) 4192

**Solution:**

Here we can write 4192 as 2 * 16 * 131

We know that the square root of 2 IS 1.414 and 16 is 4

The square root of 131 is 11.445

So the square root of 4192 = (1.414) * (4) * (11.445)

= 64.74

### (13) 4955

**Solution:**

Here we can write 4955 as 5 * 991

Here the square root of 991 is not listed in the square root table. 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,

Here the square root of 4955 = square root of 49.55 * square root of 100

Now we have to find the square root of 49.55.

We have a square root of 49 = 7 and 50 = 7.071.

Their difference is 0.071. thus, for the difference of (50 – 49), the difference in the value of the square root is 0071.

For the difference of 0.55, the difference in the value of the square root is: 0.55 * 0.071 = 0.03905.

So the square root of 49.55 = 7 + 0.03905 = 7.03905

So the square root of 4955 = (7.03905) * (10)

= 70.3905

### (14) 99/144

**Solution:**

Here we can write 99 as 9 * 11

So the square root of 99 = square root of 9 * square root of 11

= (3) * (3.316)

= 9.948

Here we know that the square root of 144 = 12

So the square root of 99/144 = 9.948/12

= 0.829

### (15) 57/169

**Solution:**

Here we can write 57 as 3 * 19

We know that the square root of 3 is 1.732 and 19 is 4.358

So the square root of 57 = (1.732) * (4.358)

= 7.548

We know that the square root of 169 is 13

So the square root of 57/169 = (7.548)/(13)

= 0.58

### (16) 101/169

**Solution:**

Here the square root of 101 is not listed in the square root table. 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,

The square root of 101 = square root of 1.01 * square root of 100

We know that the square root of 100 is 10.

Now we have to find the square root of 1.01.

We have,

Square root of 1 = 1 and square root of 2 = 1.414

Their difference is 0.414.

Thus, for the difference of 1(2 – 1), the difference in the value of the square root is 0.414.

For the difference of 0.01, the difference in the value of the square root is: 0.01 * 0.414 = 0.00414

So the square root of 1.01 = 1 + 0.00414 = 1.00414

So the square root of 101 = (1.00414) * (10)

= 10.0414

We know that the square root of 169 = 13

So the square root of 101/169 = (10.0414)/(13)

= 0.772

### (17) 13.21

**Solution:**

From the square root table, we know that

The square root of 13 is 3.606.

The square root of 14 = square root 0f 2 * square root of 7

= 1.414 * 2.645

= 3.742

Their difference is 0.136.

Thus, for the difference of 1(14 – 13), the difference in the value of the square root is 0.136. For the difference of 0.21, the difference in the value of the square root is: 0.21 * 0.136 = 0.02856

So the square root of 13.21 = 3.606 + 0.02856

= 3.635

### (18) 21.97

**Solution:**

From the square root table,

The square root of 21 = square root of 3 * square root of 7

= 1.732 * 2.645

= 4.583

The square root of 22 = square root of 2 * square root of 11

= (1.414) * (3.316)

= 4.69

Their difference is 0.107. Thus, for the difference of 1(22 – 21), the difference in the value of the square root is 0.107. For the difference of 0.97, the difference in the value of the square root is: 0.97 * 0.107 = 0.104

So the square root of 21.91 = (4.583) + (0.104)

= 4.687

### (19) 110

**Solution:**

We can write 110 as 2 * 5 * 11.

We know that the square root of 2 is 1.414 and 5 is 2.236 and 11 is 3.316.

So the square root of 110 = (1.414) * (2.236) * (3.316)

= 10.48

### (20) 1110

**Solution:**

We can write 1110 as 2 * 3 * 5 * 37

From the square root table, the square root of 2 is 1.414, and 3 is 1.732, and 5 is 2.236, and 37 is 6.083.

So the square root of 1110 = (1.414) * (1.732) * (2.236) * (6.083)

= 33.312

### (21) 11.11

**Solution:**

Here we know that the square root of 11 is 3.317 and 12 is 3.464. Their difference is 0.147.

Thus, for the difference of 1(12 – 11), the difference in the value of the square root is 0.147. For the difference of 0.11, the difference in the value of the square root is: 0.147 * 0.11 = 0.0162

So the square root of 11.11 = 3.317 + 0.0162

= 3.333

### (22) The area of a square field is 325 m^{2}. 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. Here we can write 325 as 25 * 13. We know that the square root of 25 is 5 and the square root of 13 is 3.605.

So the square root of 325 = (5) * (3.605)

= 18.03

Hence the length of one side of the field is 18.03 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:**

Now the area of rectangle = 240 * 70 = 16800m

^{2}. Given that the area of the square is equal to the area of the rectangle. So the area of the square is 16800. The length of one side of the square is the square root of its area. Here we can write 16800 as 2 * 3 * 4 * 7 * 100. We know that the square root of 2 is 1.414 and 3 is 1.732 and 4 is 2 and 7 is 2.646 and 100 is 10.So the square root of 16800 = (1.414) * (1.732) * (2) * (2.646) * (10)

= 129.6

Hence, the length of one side of the square is 129.6m.