Squares · 4-minute lesson

Square numbers ending in 5

Numbers ending in 5 have a useful pattern when you square them. Build the first part of the answer, then finish with 25.

Step by step

1. Look before the 5

   In 35, the part before the final 5 is 3.

2. Multiply by the next number

   Multiply 3 by the next whole number, 4: 3 × 4 = 12.

3. Finish with 25

   Append 25 to 12. That gives 1225, so 35 × 35 = 1225.

The pattern works with larger numbers too

For 115², use the entire part before the final 5: 11. Multiply 11 × 12 = 132, then append 25 for 13225. Appending means placing digits after a number; it is not the same as adding 25.

Why it works

A number ending in 5 can be written as 10n + 5. Its square is 100n(n + 1) + 25. That is why multiplying the leading part by its next number and appending 25 works.

Try it yourself

Work through each example before opening the answers.