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Square root calculator

Calculate the square root of any number, see the simplified radical form like 6√2, prime-factor steps, perfect-square detection, imaginary results for negatives, and a worksheet.

Practice worksheet: square root (√)

Change the worksheet number to get a different set.

  1. √106 = ________
  2. √57 = ________
  3. √86 = ________
  4. √98 = ________
  5. √81 = ________
  6. √16 = ________
  7. √9 = ________
  8. √256 = ________
  9. √25 = ________
  10. √100 = ________
  11. √60 = ________
  12. √196 = ________
  13. √40 = ________
  14. √154 = ________
  15. √151 = ________
  16. √64 = ________
  17. √36 = ________
  18. √225 = ________
  19. √54 = ________
  20. √169 = ________
Answers
  1. √106 = √106 ≈ 10.296
  2. √57 = √57 ≈ 7.55
  3. √86 = √86 ≈ 9.274
  4. √98 = 7√2 ≈ 9.899
  5. √81 = 9
  6. √16 = 4
  7. √9 = 3
  8. √256 = 16
  9. √25 = 5
  10. √100 = 10
  11. √60 = 2√15 ≈ 7.746
  12. √196 = 14
  13. √40 = 2√10 ≈ 6.325
  14. √154 = √154 ≈ 12.41
  15. √151 = √151 ≈ 12.288
  16. √64 = 8
  17. √36 = 6
  18. √225 = 15
  19. √54 = 3√6 ≈ 7.348
  20. √169 = 13

How to use

  1. Type a number.
  2. Read √n as a decimal and in exact simplified form.
  3. Use the steps to learn the method, or print the practice worksheet.

Worked example: √200 step by step

200 = 2 × 2 × 2 × 5 × 5 = 2³ × 5². Pair up: one pair of 2s and one pair of 5s leave the radical as 2 × 5 = 10. One 2 stays inside.

So √200 = 10√2 ≈ 14.1421. Check: 10 × 1.41421 = 14.1421.

Frequently asked questions

Which numbers are perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on: squares of whole numbers. Their square roots are whole numbers.

What is √(−1)?

The imaginary unit i. √(−9) = 3i. The calculator shows the imaginary form for any negative input.

How do I simplify a square root by hand?

Factor the number into primes, pull out each pair as a single factor, multiply what came out, and leave the rest inside. √48 = √(16 × 3) = 4√3.

Why is √2 irrational?

Its decimal never ends or repeats, so no fraction equals it exactly. The decimal shown is rounded to the precision you choose.

What about decimals like √2.25?

Decimal inputs give a decimal result (1.5). Exact radical simplification applies to whole numbers.

Can I print a worksheet?

Yes. Twenty mixed problems with an answer key, regenerated by changing the worksheet number.

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