Find the square root of :
`0.2916`

Answer

To find the square root of 0.2916 using the long division method, we can follow these steps:

### Step 1: Pair the digits
Start by pairing the digits of the number from the decimal point. For 0.2916, we can pair them as follows:
- (0) (29) (16)

### Step 2: Find the largest square
Now, we look for the largest square number that is less than or equal to the first pair (0). The largest square is 0 (since 0² = 0).

### Step 3: Subtract and bring down the next pair
Subtract 0 from 0, which gives us 0. Now, bring down the next pair (29) next to it. We now have 0 (from the first pair) and 29.

### Step 4: Double the divisor
Double the current result (which is 0). So, 0 × 2 = 0. We will denote this as our new divisor.

### Step 5: Find the next digit
Now, we need to find a digit (let's call it 'x') such that (0x) × x is less than or equal to 29.
- Trying 5: (05) × 5 = 25
- Trying 6: (06) × 6 = 36 (too high)

So, we take 5. Now, we have:
- Current result: 0.5
- Subtract 25 from 29: 29 - 25 = 4

### Step 6: Bring down the next pair
Now, bring down the next pair (16) next to the remainder (4). We now have 416.

### Step 7: Double the current result
Double the current result (which is 0.5). So, 0.5 × 2 = 1.

### Step 8: Find the next digit
Now, we need to find a digit (let's call it 'y') such that (1y) × y is less than or equal to 416.
- Trying 3: (13) × 3 = 39
- Trying 4: (14) × 4 = 56
- Trying 5: (15) × 5 = 75
- Trying 6: (16) × 6 = 96
- Trying 7: (17) × 7 = 119
- Trying 8: (18) × 8 = 144
- Trying 9: (19) × 9 = 171
- Trying 10: (20) × 10 = 200
- Trying 11: (21) × 11 = 231
- Trying 12: (22) × 12 = 264
- Trying 13: (23) × 13 = 299
- Trying 14: (24) × 14 = 336
- Trying 15: (25) × 15 = 375
- Trying 16: (26) × 16 = 416

So, we take 6. Now, we have:
- Current result: 0.54
- Subtract 416 from 416: 416 - 416 = 0

### Final Result
Since we have no remainder left, the square root of 0.2916 is **0.54**.

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