Practice30Create account

Ankit says: ', and both primes appear in the factorisation, so 6125 must be a perfect square.' Which correction is right?

Class 8Squares and Square RootsSquares and Roots
  • A6125 becomes a perfect square as soon as it is divided by 7.
  • BThe prime 5 appears three times — an odd count — so 6125 is not a perfect square.
  • CAnkit is right: .
  • D6125 is not a perfect square because it ends in 5.

Step-by-Step Solution

For a perfect square EVERY prime must appear an even number of times; here 5 appears three times, so 6125 is not a square and straddle it). Dividing by 7 leaves , still not a square. And , not 6125. The last option reaches the right conclusion for a wrong reason: ending in 5 is perfectly allowed for squares — 25, 225 and 625 all end in 5.
Answer: B) The prime 5 appears three times — an odd count — so 6125 is not a perfect square.

Key idea: Properties of perfect squares

Useful patterns to spot a perfect square (and reject non-squares):

- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square ; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + . Try it: .

These let you reject many candidates without doing any heavy work.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Squares and Square Roots practice questions

More Class 8 Squares and Square Roots practice

Given that √225 = 15 and √64 = 8, find √225 × 64.Given that 5.8² = 33.64 and 5.9² = 34.81, which is the better estimate of √34 correct to…The floor of a square room has an area of 1936 m². Square tiles of side 2 m are laid in…The table shows the units digit of a square for each possible units digit of a number.…The picture builds a 4 × 4 square from L-shaped layers of 1, 3, 5 and 7 small squares.…