How to Square Numbers from 991 to 1000 Fast: Easy Mental Math Trick

 

Can you calculate 991², 995², or 1000² without long multiplication? Yes. Numbers from 991 to 1000 are just below 1000, so their squares follow a simple pattern that is easy to calculate mentally.

In this Maths Tricks guide, you will learn how to square numbers close to 1000. The method uses the identity (1000 − d)², where d is the small amount subtracted from 1000.

The Quick Pattern: 991² to 1000²

Every number from 991 to 1000 can be written as 1000 minus a small number. The leading part decreases by 2 each time, while the final two digits follow the squares of 9 down to 0:

991² = 982081   |   992² = 984064   |   993² = 986049

994² = 988036   |   995² = 990025   |   996² = 992016

997² = 994009   |   998² = 996004   |   999² = 998001

1000² = 1000000

The Main Shortcut: Use 1000 as the Base

Write the number as 1000 − d. Then expand the square:

(1000 − d)² = 1000000 − 2000d + d²

This comes from the algebra rule (a − b)² = a² − 2ab + b². Because 1000² is 1,000,000, the arithmetic is easy to organize.

Example 1: Find 991²

991 is 1000 − 9, so use d = 9:

991² = 1000000 − (2000 × 9) + 9²

1000000 − 18000 + 81 = 982081

Example 2: Find 995²

995 is 1000 − 5, so use d = 5:

995² = 1000000 − (2000 × 5) + 5²

1000000 − 10000 + 25 = 990025

Example 3: Find 998²

998 is 1000 − 2, so use d = 2:

998² = 1000000 − (2000 × 2) + 2²

1000000 − 4000 + 4 = 996004

The Complete 991–1000 Square Table

Number	Write As	Square
991	1000 − 9	982,081
992	1000 − 8	984,064
993	1000 − 7	986,049
994	1000 − 6	988,036
995	1000 − 5	990,025
996	1000 − 4	992,016
997	1000 − 3	994,009
998	1000 − 2	996,004
999	1000 − 1	998,001
1000	1000 − 0	1,000,000

Why the Pattern Works

Each number is close to 1000, so the distance d is small. The term 2000d controls the main decrease from 1,000,000, while d² supplies the final two digits: 81, 64, 49, 36, 25, 16, 09, 04, 01, and 00.

d = 9, 8, ... 0 → d² = 81, 64, ... 00

Common Mistakes to Avoid

Do not subtract only 2d from 1000. The correct middle term is 2000d because the base is 1000. Also keep leading zeros in endings such as 09, 04, and 01.

Always estimate your answer. A number slightly below 1000 should have a square slightly below 1,000,000. This quick check helps catch missing digits and misplaced zeros.

Practice Problems

Try these without a calculator:

1. 992²
2. 994²
3. 996²
4. 998²
5. 1000²

Answer Key

1. 992² = 984,064
2. 994² = 988,036
3. 996² = 992,016
4. 998² = 996,004
5. 1000² = 1,000,000

Final Takeaway

To square a number from 991 to 1000, write it as 1000 − d and use:

(1000 − d)² = 1000000 − 2000d + d²

This shortcut makes the 991–1000 square table easier to remember and helps you solve mental-math questions more confidently. Save this Maths Tricks guide for homework, quiz review, and fast calculations.

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