Find the square root of :
`0.602` correct to two places of decimal.

Answer

To find the square root of \(0.602\) correct to two decimal places, we can use the long division method for square roots. Here’s a step-by-step solution:

### Step 1: Prepare the number
First, we write the number \(0.602\) in a form that makes it easier to work with. We can add two zeros to the right of the decimal point to make it \(0.60200\).

### Step 2: Group the digits
Starting from the decimal point, we group the digits in pairs. For \(0.60200\), we have:
- The first group is \(0\) (before the decimal).
- The second group is \(60\).
- The third group is \(20\).

So, we have the groups: \(0 | 60 | 20\).

### Step 3: Find the largest square
Now, we find the largest square less than or equal to the first group \(0\):
- The largest square is \(0^2 = 0\).
- We write \(0\) above the line.

### Step 4: Subtract and bring down the next group
Subtract \(0\) from \(0\):
\[ 0 - 0 = 0 \]
Now, bring down the next group \(60\) to make it \(60\).

### Step 5: Double the current result
Double the number above the line (which is \(0\)):
\[ 2 \times 0 = 0 \]
We write \(0\) next to the \(60\) and find a digit \(x\) such that:
\[ 0x \times x \leq 60 \]
Trying \(7\):
\[ 07 \times 7 = 49 \]
This works since \(49 \leq 60\).

### Step 6: Write the result and subtract
Write \(7\) above the line:
\[ 0.7 \]
Now, subtract \(49\) from \(60\):
\[ 60 - 49 = 11 \]
Bring down the next group \(20\) to make it \(1120\).

### Step 7: Double the current result again
Double the current result \(0.7\):
\[ 2 \times 7 = 14 \]
Now, we need to find a digit \(y\) such that:
\[ 14y \times y \leq 1120 \]
Trying \(8\):
\[ 148 \times 8 = 1184 \]
This is too high. Trying \(7\):
\[ 147 \times 7 = 1029 \]
This works since \(1029 \leq 1120\).

### Step 8: Write the result and subtract again
Write \(7\) next to the previous result:
\[ 0.77 \]
Now, subtract \(1029\) from \(1120\):
\[ 1120 - 1029 = 91 \]

### Step 9: Finalize the square root
Since we are looking for the square root correct to two decimal places, we can stop here. Thus, the square root of \(0.602\) is approximately:
\[ \sqrt{0.602} \approx 0.77 \]

### Summary
The square root of \(0.602\) correct to two decimal places is \(0.77\).

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