Mental Math · Level Up · L2
To square any number, anchor it to the nearest ten. Multiply the easy pair (anchor × its mirror) and add the square of the gap. It turns 47² into 50 × 44 + 9.
Watch the method
47² : the nearest ten is 50. Go 3 the other way to 44. Then 50 × 44 = 2200, and add the gap squared, 3² = 9, to get 2209.
The nearest ten to 47 is 50.
Go 3 the other way to get the partner 44.
Multiply that easy pair.
Add the gap squared (3²).
Your turn
Use the method, then check. Stuck? Reveal the steps.
Any square n² equals (n−d)(n+d) + d², where d is the distance to a round anchor. Choosing the anchor at a ten makes the product trivial, and d is small so d² is easy.
Why it works
Squares hide a difference of squares: nudge one factor down and the other up by the same amount, then correct.
29²
Anchor
Nearest ten is 30; gap 1.
Pair
30 × 28 = 840.
Add gap²
840 + 1 = 841.
47²
Anchor
Nearest ten is 50; gap 3.
Pair
50 × 44 = 2200.
Add gap²
2200 + 9 = 2209.
84²
Anchor
Nearest ten is 80; gap 4.
Pair
80 × 88 = 7040.
Add gap²
7040 + 16 = 7056.
Forgetting to add the gap squared.
50 × 44 is only part of it. You must add d² (here 9) to reach 2209.
Moving both factors the same direction.
One goes up, the other down by the same gap. 47 → 50 means the partner is 44, not 50.
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).47² = ?
63² = ?
84² = ?
38² = ?
52² = ?
96² = ?
29² = ?
71² = ?
88² = ?
67² = ?
93² = ?
56² = ?