The square root of `36/5` when corrected to two decimal places is

Options

A. 2.68
B. 2.69
C. 2.67
D. 2.66

Explanation

To find the square root of \( \frac{36}{5} \) corrected to two decimal places, we can follow these steps:

### Step 1: Calculate \( \frac{36}{5} \)
First, we need to divide 36 by 5.

\[ \frac{36}{5} = 7.2 \]

### Step 2: Find the square root of 7.2
Now, we will find the square root of 7.2 using the long division method.

### Step 3: Set up the long division
We will set up the long division for the square root of 7.2. To do this, we can write 7.2 as 7.20 (adding two zeros for decimal places).

```
____
√7.20
```

### Step 4: Pair the digits
We will pair the digits starting from the decimal point. The pairs are (7) and (20).

### Step 5: Find the largest square less than or equal to 7
The largest square less than or equal to 7 is 4 (which is \( 2^2 \)). So we write 2 above the line.

```
2
____
√7.20
```

### Step 6: Subtract and bring down the next pair
Subtract \( 4 \) from \( 7 \) to get \( 3 \), and then bring down the next pair (20) to make it 320.

```
2
____
√7.20
4
----
32
```

### Step 7: Find the next digit
Now, we need to find a digit \( x \) such that \( (20 + x) \times x \) is less than or equal to 320.

Testing \( x = 6 \):
\[ (20 + 6) \times 6 = 26 \times 6 = 156 \quad (\text{which is less than } 320) \]

Testing \( x = 7 \):
\[ (20 + 7) \times 7 = 27 \times 7 = 189 \quad (\text{which is less than } 320) \]

Testing \( x = 8 \):
\[ (20 + 8) \times 8 = 28 \times 8 = 224 \quad (\text{which is less than } 320) \]

Testing \( x = 9 \):
\[ (20 + 9) \times 9 = 29 \times 9 = 261 \quad (\text{which is less than } 320) \]

Testing \( x = 10 \):
\[ (20 + 10) \times 10 = 30 \times 10 = 300 \quad (\text{which is less than } 320) \]

Testing \( x = 11 \):
\[ (20 + 11) \times 11 = 31 \times 11 = 341 \quad (\text{which is greater than } 320) \]

So, we take \( x = 10 \).

### Step 8: Write the next digit
Now we write 10 above the line:

```
2.6
____
√7.20
4
----
32
300
----
20
```

### Step 9: Bring down another pair of zeros
Bring down another pair of zeros to make it \( 2000 \).

### Step 10: Find the next digit again
Now we need to find \( y \) such that \( (260 + y) \times y \) is less than or equal to 2000.

Testing \( y = 7 \):
\[ (260 + 7) \times 7 = 267 \times 7 = 1869 \quad (\text{which is less than } 2000) \]

Testing \( y = 8 \):
\[ (260 + 8) \times 8 = 268 \times 8 = 2144 \quad (\text{which is greater than } 2000) \]

So we take \( y = 7 \).

### Step 11: Finalizing the answer
Now we write 7 above the line:

```
2.68
____
√7.20
4
----
32
300
----
2000
1869
----
131
```

### Conclusion
The square root of \( \frac{36}{5} \) is approximately \( 2.68 \) when corrected to two decimal places.