For Republic Day, 324 cadets stand in a square formation, with as many rows as cadets in each row. How many cadets are in each row?
Class 8Squares and Square RootsSquares and Roots
A162
B81
C36
D18
Step-by-Step Solution
In a square formation the total is (cadetsperrow)2.324=18 because 18×18=324.
Answer: D) 18
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: 324. Factorise: 324=22×34=(2×3×3)2. So 324=2×3×3=18.
Example: 576. Factorise: 576=26×32=(23×3)2. So 576=8×3=24.
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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