Evaluate the following :
`(31)/(sqrt(1681))`

Answer

To evaluate the expression \( \frac{31}{\sqrt{1681}} \), we can follow these steps:

### Step 1: Find the square root of 1681
We need to determine \( \sqrt{1681} \). To do this, we can look for a number that, when multiplied by itself, equals 1681.

### Step 2: Identify the perfect square
To find the square root, we can check numbers systematically. We notice that:
- \( 1 \times 1 = 1 \)
- \( 2 \times 2 = 4 \)
- \( 3 \times 3 = 9 \)
- \( 4 \times 4 = 16 \)
- \( 5 \times 5 = 25 \)
- \( 6 \times 6 = 36 \)
- \( 7 \times 7 = 49 \)
- \( 8 \times 8 = 64 \)
- \( 9 \times 9 = 81 \)
- \( 10 \times 10 = 100 \)
- \( 11 \times 11 = 121 \)
- \( 12 \times 12 = 144 \)
- \( 13 \times 13 = 169 \)
- \( 14 \times 14 = 196 \)
- \( 15 \times 15 = 225 \)
- \( 16 \times 16 = 256 \)
- \( 17 \times 17 = 289 \)
- \( 18 \times 18 = 324 \)
- \( 19 \times 19 = 361 \)
- \( 20 \times 20 = 400 \)
- \( 21 \times 21 = 441 \)
- \( 22 \times 22 = 484 \)
- \( 23 \times 23 = 529 \)
- \( 24 \times 24 = 576 \)
- \( 25 \times 25 = 625 \)
- \( 26 \times 26 = 676 \)
- \( 27 \times 27 = 729 \)
- \( 28 \times 28 = 784 \)
- \( 29 \times 29 = 841 \)
- \( 30 \times 30 = 900 \)
- \( 31 \times 31 = 961 \)
- \( 32 \times 32 = 1024 \)
- \( 33 \times 33 = 1089 \)
- \( 34 \times 34 = 1156 \)
- \( 35 \times 35 = 1225 \)
- \( 36 \times 36 = 1296 \)
- \( 37 \times 37 = 1369 \)
- \( 38 \times 38 = 1444 \)
- \( 39 \times 39 = 1521 \)
- \( 40 \times 40 = 1600 \)
- \( 41 \times 41 = 1681 \)

Thus, we find that \( \sqrt{1681} = 41 \).

### Step 3: Substitute back into the expression
Now that we have found \( \sqrt{1681} = 41 \), we can substitute this back into our original expression:
\[ \frac{31}{\sqrt{1681}} = \frac{31}{41} \]

### Step 4: Final answer
The final answer is:
\[ \frac{31}{41} \]

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