Question 1
55² = ?
Squaring a number ending in 5 — beat the clock.
- 2525
- 3025
- 3021
- 3019
- 3013
Show the worked solution
- Ends in 5 — Ekadhikena: take 5, multiply by one more: 5 × 6 = 30.
- Append 25: 30 | 25 → 3025.
- Answer: 3025.
Ekadhikena / Yavadunam
How to square numbers fast — two sutras cover almost everything
To learn how to square numbers fast, two patterns cover most exam cases. A number ending in 5: multiply the leading part by one more than itself and append 25, so 75² is 7 × 8 = 56 then 25, giving 5625. A number near 100: add its surplus to itself for the front, and square the surplus for the back.
Squaring appears constantly — in mensuration, in quadratic comparison, in approximation and in simplification — so a candidate who squares instantly saves seconds many times per paper rather than once. These two sutras are also the easiest Vedic techniques to learn, which makes them the right entry point.
Try it against the clock. Vedic Squaring runs at 15s easy, 20s medium and 30s hard. The clock is stamped and judged on our server, so the limit you see is the deadline that is actually enforced — and it starts when you tap Start, not while the question is loading.
How to square numbers fast with Ekadhikena and Yavadunam
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Numbers ending in 5 — Ekadhikena
Take everything before the 5, multiply it by one more than itself, and write 25 after it. For 75²: 7 × 8 = 56, then 25, giving 5625. For 115²: 11 × 12 = 132, then 25, giving 13225. It works for any length.
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Numbers just above 100 — Yavadunam
For 108²: the surplus is 8, so add it to the number for the front (108 + 8 = 116) and square it for the back (64), giving 11664. The back always occupies two digits for base 100 — pad with a zero if the square is single-digit.
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Numbers just below 100 — the same rule with a deficit
For 88²: the deficit is 12, so subtract it (88 − 12 = 76) and square it (144). Since 144 exceeds two digits, carry the 1: 76 + 1 = 77, then 44, giving 7744.
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Everything else — crosswise
When neither pattern applies, square with the general crosswise method, which is just multiplication of the number by itself. Knowing when a shortcut does NOT apply is as valuable as knowing the shortcut.
Which squaring pattern applies
| The number | Method |
|---|---|
| Ends in 5 (75, 115) | n(n+1) then append 25 |
| Just above 100 (108) | Add surplus, then square it |
| Just below 100 (88) | Subtract deficit, then square it, carry if needed |
| Near 50 | Same idea with base 50 — halve the adjustment |
| Near 1000 | Same idea, back part takes three digits |
| Anything else | Crosswise multiplication |
3 real how to square numbers fast, with worked solutions
Generated by the same engine that mints the Quant Daily daily. Each answer is computed from the numbers printed in the question, and the walkthrough below each one is the engine's own working — not a solution written afterwards. Reload this page's live drill and you get different numbers.
Question 2
104² = ?
Squaring near a base — beat the clock.
- 10016
- 10916
- 10816
- 10800
- 10820
Show the worked solution
- 104 is 4 above 100 — Yavadunam: go the surplus again: 104 + 4 = 108.
- Append the surplus squared in 2 digits: 4² = 16 → 108 | 16 → 10816.
- Answer: 10816.
Question 3
105² = ?
Squaring a number ending in 5 — beat the clock.
- 10025
- 11012
- 11013
- 11022
- 11025
Show the worked solution
- Ends in 5 — Ekadhikena: take 10, multiply by one more: 10 × 11 = 110.
- Append 25: 110 | 25 → 11025.
- Answer: 11025.
Common mistakes this drill is built from
The wrong options are not random numbers. Each one is the result of a specific careless error for this topic, so picking one tells you which habit is costing you marks.
Not padding the back part to the right width
For base 100 the back is two digits. 103² is 106 then 09 — writing 1069 instead of 10609 is the classic slip, and it comes from forgetting the pad rather than from the method.
Missing the carry when the back part overflows
88² gives a back part of 144, which is three digits for a two-digit slot. The extra 1 carries into the front. Skipping the carry is off by exactly 100.
Forcing a sutra where it does not fit
These patterns apply to specific shapes. Spending time checking whether one applies to 63² costs more than simply squaring it crosswise.
Why your answer came out wrong
The specific wrong numbers this topic produces, and what each one tells you about the step you took. If you have just got a question wrong and want to know which habit did it, start here.
My square of a number near 100 is out by exactly a hundred — why?
The back half was not padded to two digits. For 103, the front is 103 + 3 = 106 and the back is 3² = 9, which must be written as 09, giving 10609. Writing 1069 loses a place, and the same rule applies below the base: 96² is 92 | 16 = 9216.
What do I do when the back half comes out as three digits?
Carry the overflow into the front. For 88², the deficit from 100 is 12, the front is 88 − 12 = 76 and the back is 12² = 144. Keep 44 and carry the 1: 77 | 44 = 7744. Dropping that carry gives a number that is not even the right length.
Does the ending-in-5 rule work for 145 as well as 45?
Yes, for any number ending in 5. Multiply the leading part by one more than itself and write 25 behind it: 45² = 4 × 5 | 25 = 2025, and 145² = 14 × 15 | 25 = 21025. It works only for numbers ending in 5, and forcing it onto 46 is what makes people distrust the whole method.
FAQ
How do I square a number ending in 5 instantly?
Multiply the part before the 5 by one more than itself, then write 25 after it. For 65²: 6 × 7 = 42, then 25, giving 4225. This works for any length — 205² is 20 × 21 = 420 followed by 25, or 42025.
How do I square a number near 100?
Take the surplus or deficit from 100. For 108, the surplus is 8: add it to the number for the front (116) and square it for the back (64), giving 11664. For 88, the deficit is 12: subtract for the front (76) and square for the back (144), carrying the extra digit to give 7744.
Are these worth learning for the exam?
The ending-in-5 rule certainly — it is a few minutes to learn and applies often. The near-base rule is worth it once the first is automatic. Both need timed drilling before they beat ordinary squaring, which is what the clocked practice below is for.
Practise the next topic
- All 23 drill types — the full rotation with every published time limit.
- Vedic maths multiplication tricks — crosswise — vedic maths multiplication tricks, timed.
- Square root and cube root questions — read the answer off the last digit — square root and cube root questions, timed.
- Vedic maths shortcuts — the seven sutras that make a 15-second answer possible.
- How to improve calculation speed — the six-week arc these drills fit into.
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