**High School Number Sense Lesson 71: Square Root Memorization**

Sometimes memorization is the key to success on number sense questions. Today's concept appeared

**13 times**last year, with a median placement at

**question # 71**.

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A student who wants to succeed with these questions need only memorize 7 square roots--ranging from 2 to 10 (excluding 4 and 9, which ought to be automatic by now). I will show each one truncated to 4 decimal places, because I haven't seen a number sense question that requires more than that. In fact, most questions require knowledge of only two or three decimal places.

**√2: 1.4142**

√3: 1.7320

√5: 2.2360

√6: 2.4494

√7: 2.6457

√8: 2.8284

√10: 3.1622

√3: 1.7320

√5: 2.2360

√6: 2.4494

√7: 2.6457

√8: 2.8284

√10: 3.1622

**Example 1: What is the value of √5 rounded to the 1/10's place? ___**

- √5 is about 2.2360.
- Round to the tenths place:
**2.2**

**Example 2: Truncate √2 to the tenths place. ___**

- √2 is about 1.4142.
- Truncate to (remove everything after) the tenths place:
**1.4**

**Example 3: Round √8 to the hundredths place. ___**

- √8 is about 2.8284.
- Round to the hundredths place:
**2.83**

**Example 4: Round √3 + √6 to the tenths place. ___**

- √3 is about 1.7320. √6 is about 2.4494.
- Round to 2 decimal places of each, and add: 1.73 + 2.45 = 4.18
- Round to the tenths place:
**4.2**

**Example 5: Truncate 7√7 to a whole number. ___**

- √7 is about 2.6457.
- Worry only about the first decimal place, and multiply: 7 x 2.6 = 18.2
- Truncate to a whole number:
**18**

**Example 5 (take 2): Truncate 7√7 to a whole number. ___**

- Bring the whole number inside the radicand (√) by squaring it: 7√7 =
**√343**. - Think of the largest perfect square less than or equal to 343:
**324**. - √324 =
**18**

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

**Up Next for High School: RemainPolynom**