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At a school function the students stand so that the number of rows equals the number of students in each row. If there are 57 rows, how many students are on the ground altogether?

Class 8Squares and Square RootsSquares and Roots
  • A114
  • B3481
  • C3249
  • D3149

Step-by-Step Solution

Rows = columns = 57, so the total is . The trap 114 doubles 57 instead of squaring it. The trap 3481 is , the square of the wrong number, and 3149 comes from a carrying slip while multiplying .
Answer: C) 3249

Key idea: Square root by prime factorisation

**Step 1**: factorise the number into primes.
**Step 2**: pair up identical factors.
**Step 3**: from each pair, take ONE factor — the product is the square root.

Example: . Factorise: . So .

Example: . Factorise: . So .

If any prime appears an odd number of times, the number isn't a perfect square — and you'd need to multiply (or divide) by that prime to make it one.

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