**High School Number Sense Lesson 97: Squaring a Number between 31 & 40**

This concept showed up

**5 times**this year, with a median placement at

**question # 8**.

**Like our Facebook Page (**

**https://www.facebook.com/numberdojo/**

**) if you want to see new number sense posts on your wall. I will reward you with a free concept index or flashcard file of your choice. Thank you!**

**Number Dojo Level: 189**

Like

**Square11-20**and

**Square21-30**, it is probably best to memorize the squares of these numbers. There are a couple of problems with this strategy though:

- The bigger numbers are a little more difficult to memorize.
- These problems appear far less often, so the low frequency will hinder the student’s memory.

If needed, quickly try to FOIL the numbers to find the product. I will demonstrate this in each example because I can’t very well demonstrate how to pluck the perfect square out of my memory…

**Example 1: 31 x 31 = ___**

- Memorize or FOIL: (31 x 31).
**L**: 1 x 1 =**1**; write this down.**OI**: (3 x 1) x 2 = 3 x 2 =**6**; write this down in front.**F**: 3 x 3 =**9**; write this in front. The answer is**961**.

**Example 2: 34 x 34 = ___**

- Memorize or FOIL.
**L**: 4 x 4 =**16**; write the**6**and regroup the**1**.**OI**: (3 x 4) x 2 = 12 x 2 =**24**; + the regrouped 1 =**25**. Write the**5**in front and regroup the**2**.**F**: 3 x 3 =**9**, + the regrouped 2 =**11**. Write this in front. The answer is**1156**.

**Example 3: 37 x 37 = ___**

- Memorize or FOIL.
**L**: 7 x 7 =**49**; write the**9**and regroup the**4**.**OI**: (3 x 7) x 2 = 21 x 2 =**42**; + the regrouped 4 =**46**. Write the**6**in front and regroup the**4**.**F**: 3 x 3 =**9**, + the regrouped 4 =**13**. Write this in front. The answer is**1369**.

**Example 4: 36 x 36 = ___**

- Memorize or FOIL.
**L**: 6 x 6 =**36**; write the**6**and regroup the**3**.**OI**: (3 x 6) x 2 = 18 x 2 =**36**; + the regrouped 3 =**39**. Write the**9**in front and regroup the**3**.**F**: 3 x 3 =**9**, + the regrouped 3 =**12**. Write this in front. The answer is**1296**.

**Example 5: 32 x 32 = ___**

- This happens to be
**2^10**, which should also be memorized. **L**: 2 x 2 =**4**; write this down.**OI**: (3 x 2) x 2 = 6 x 2 =**12**; write the**2**and regroup the**1**.**F**: 3 x 3 =**9**, + the regrouped 1 =**10**. Write this in front. The answer is**1024**.

**Up Next for High School: ConvMetricOp**