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Finding Squares and Square Roots Quiz - CBSE Class 8 Mathematics

Free practice quiz: Finding Squares and Square Roots (CBSE Class 8 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 20 multiple-choice questions on Finding Squares and Square Roots, and 20 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Start quiz: 20 questions, free

Learn the key ideas first ↓

Learn the key ideas Beta

What a square means

  • The square of a number is the number multiplied by itself.
  • Squaring is not doubling. Doubling adds a number to itself, while squaring multiplies it by itself.
Definition of square
\[n^2 = n \times n\]
Square of a product
\[(ab)^2 = a^2 b^2\]

Common mistake: Writing n^2 as 2 \times n, which doubles the number instead of multiplying it by itself.

Squaring big numbers using identities

  • Split a big number into a round number plus or minus a small number.
  • Then use an identity so each part is easy to square in your head.
Square of a sum
\[(a+b)^2 = a^2 + 2ab + b^2\]
Square of a difference
\[(a-b)^2 = a^2 - 2ab + b^2\]

Common mistake: Forgetting the middle term 2ab and writing (a+b)^2 = a^2 + b^2.

Square root by prime factorisation

  • Break the number into prime factors and group equal primes into pairs.
  • Take one prime from each pair and multiply them to get the square root.
  • If any prime is left without a pair, the number is not a perfect square.
Root undoes square
\[\sqrt{a^2} = a\]
Root of a product
\[\sqrt{ab} = \sqrt{a} \times \sqrt{b}\]

Common mistake: Multiplying both primes of every pair, which gives back the original number instead of its square root.

Long division and digit clues

  • Pair the digits from the right using bars. Each bar gives one digit of the square root.
  • The units digit of the square gives clues about the root's last digit. Ending 4 gives 2 or 8. Ending 6 gives 4 or 6.
Digits in root, n even
\[\text{digits in } \sqrt{N} = \frac{n}{2}\]
Digits in root, n odd
\[\text{digits in } \sqrt{N} = \frac{n+1}{2}\]

Common mistake: Pairing the digits from the left instead of from the right, which gives the wrong number of digits in the root.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the square of 5?

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    Answer: C. 25

    The square of a number is the number multiplied by itself. 5 x 5 = 25

  2. What is the square of 23?

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    Answer: B. 529

    23 multiplied by itself: 23 x 23 = 529

  3. Find the square of 67.

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    Answer: B. 4489

    67 x 67 = 4489

  4. What is the square of 112?

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    Answer: A. 12544

    112 x 112 = 12544

  5. Find the square of 203.

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    Answer: B. 41209

    203 x 203 = 41209

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What is the square root of 16?
  2. Calculate 12²
  3. Find √81
  4. Find the square root of 225
  5. Calculate 35²
  6. What is √625?
  7. What is √1296?
  8. Calculate 98²
  9. Find √2809
  10. Find the square root of 6561
  11. Calculate 147²
  12. What is √10201?
  13. What is √16129?
  14. Calculate the square of 297.
  15. Find the square root of 99856.

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