**Middle School Number Sense Lesson 75: Squaring a 3-Digit Number**

A couple of months ago we learned how to multiply two 3-digit numbers using a modified FOIL method (

**FOIL3by3Digit**). Today's lesson is easier by several steps. It appeared

**5 times**on last year's tests, with a median placement at

**question # 73**.

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The reason these questions are a bit easier than multiplying any 3-digit numbers is because they almost always have the digit

**0**in the middle (like 307 x 307).

**How to Solve:**

- Look at the last 2 digits of the number and square them. Write the result down as a 2-digit number. (If it is more than 2 digits, write down the last 2 digits and regroup the first).
- From the original number, multiply the hundreds digit by the last 2 digits, and double this product. (Add any regrouping from Step 1). Write this down as a 2-digit number in front. (If it is more than 2 digits, write down the last 2 digits and regroup the first).
- Square the hundreds digit (adding any regrouping from Step 2), and write this down in front.

**Example 1: 402 x 402 = ___**

- Square the last 2 digits. 02 x 02 =
**04**; write this down. - Multiply
**4 x 02**(which is 08) and double it:**16**; write this down in front. - Square the hundreds digit: 4 x 4 =
**16**; write this down in front. - The answer is
**161604**.

**Example 2: 307 x 307 = ___**

- Square the last 2 digits:
**49**; write this down. - Multiply
**3 x 07**(which is 21) and double it:**42**; write this down in front. - Square the hundreds digit: 3 x 3 =
**9**; write this down in front. - The answer is
**94249**.

**Example 3:**

**904**

^{2}= ___1. Square the last 2 digits:

**16**; write this down.

2. Multiply

**9 x 04**(which is 36) and double it:

**72**; write this in front.

3. Square the hundreds digit:

**81**; write this in front.

4. The answer is

**817216**.

**Example 4:**

**506**

^{2}= ___1. Square the last 2 digits:

**36**; write this down.

2. Multiply

**5 x 06**(which is 30) and double it:

**60**; write this in front.

3. Square the hundreds digit:

**25**; write this in front.

4. The answer is

**256036**.

**Example 5: 212 x 212 = ___**

- Square the last 2 digits:
**144**; write the**44**and regroup the**1**. - Multiply
**2 x 12**(which is 24) and double it:**48**. Add the regrouped**1**and write this in front:**49**. - Square the hundreds digit:
**4**; write this in front. - The answer is
**44944**.

**Example 6: 908 x 908 = ___**

- Square the last 2 digits:
**64**; write this down. - Multiply
**9 x 08**(which is 72) and double it:**144**. Write**44**in front and regroup the**1**. - Square the hundreds digit:
**81**. Add the regrouped**1**and write this in front:**82**. - The answer is
**824464**.

**Check back soon for a free worksheet to help you practice Square3Digit.**

**Up Next for Middle School: DiscrimRoot**