#### Transcript of Estimate Irrational Numbers & Expressions

**Estimate Irrational Numbers & Expressions**

The value of an irrational number or expression that contains a square root can be estimated as between two rational numbers by finding that the square of the irrational number or expression is between the squares of the two rational numbers.

The value of an irrational number or expression that contains a cube root can be estimated as between two rational numbers by finding that the cube of the irrational number or expression is between the cubes of the two rational numbers.

Example 2:

Example1:

Determine which two values the following number is between.

3.5 and 3.6

3.6 and 3.7

3.7 and 3.8

3.8 and 3.9

First, square the given number.

Next, calculate the squares of each number from the answer choices.

Then, determine which two values the number 15 is between. Since 15 is between 14.44 and 15.21, is between and .

Therefore, is between 3.8 and 3.9.

Determine which two values the following expression is between.

32 and 33

33 and 34

34 and 35

35 and 36

Solution:

First, cube the given expression.

Next, calculate the cubes of each number from the answer choices.

Then,

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