**High School Number Sense Lesson 67: Greatest Integer Function**

Today's concept is simple to understand, but some of the problems may be a little difficult to solve. It appeared

**10 times**on high school tests last year, with a median appearance at

**question # 64**.

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The

**Greatest Integer Function**is represented with brackets [ ], like this:

**f(x) = [x]**

**greatest integer less than or equal to**whatever is inside the brackets. There are two basic things to remember with these problems:

- If the number inside the [ ] is an integer, simply write it down.
- If the number inside the [ ] is not an integer,
**round down**to the nearest integer.

**Example 1: The Greatest Integer Function is written as f(x) = [x]. Find f[√2].**

**√2**is somewhere between**1**(which is √1) and**2**(which is √4).- Round down to the nearest integer, which is
**1**. - (Number sense coaches recommend that each student memorize the first 10 square roots, up to 4 digits. So you may have √2 memorized, which is about
**1.4142**.)

**Example 2: The Greatest Integer Function is written as f(x) = [x]. Find f[√10].**

**√10**is somewhere between**3**(which is √9) and**4**(which is √16).- Round down to the nearest integer, which is
**3**. - (You may already have √10 memorized, which is about
**3.1622**).

**Example 3: The Greatest Integer Function is written as f(x) = [x]. Find f[√2 + √3 + √5].**

**√2**is about 1.41.**√3**is about 1.73.**√5**is about 2.23.- 1.41 + 1.73 + 2.23 =
**5.37**. Round down to the nearest integer, which is**5**.

**Example 4: The Greatest Integer Function is written as f(x) = [x]. Find [5√5].**

- Instead of multiplying 5 by your memorized value of √5, it is probably easier to bring the 5 (in front of the √) inside the √ by squaring it. This makes 5√5 = √125.
**√125**is somewhere between**11**(which is √121) and**12**(which is √144).- Round down to the nearest integer, which is
**11**.

**Example 5: The Greatest Integer Function is written as f(x) = [x]. Find π√10. ___**

**π**is about 3.14.**√10**is about 3.1622. Their product is just under 10.- Round down to the nearest integer, which is
**9**.

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

**Up Next for High School: ProbCoin**