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Common Core for Grade 8

Common Core for Mathematics

More Math Lessons for Grade 8

Videos, examples, solutions, and lessons to help Grade 8 students learn how to use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π^{2}).

*For example, by truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations*.

Common Core: 8.NS.2

- I can approximate irrational numbers as rational numbers
- I can approximately locate irrational numbers on a number line
- I can estimate the value of expression involving irrational numbers using rational numbers.

(Examples: Being able to determine the value of the √2 on a number line lies between 1 and 2, more accurately, between 1.4 and 1.5, and more accurately, etc.) - I can compare the size of irrational numbers using rational approximations. The following table gives the perfect squares of numbers from 1 to 15. Scroll down the page to learn how to approximate irrational numbers using the perfect squares.

**How to approximately locate irrational numbers on a number line**

Learn the perfect squares for the numbers 1 to 15.

Examples:

Approximate the square root to the nearest integer and place your answer on the number line.

√23

-√10

Evaluate the expression

2√(a + b^{2}) when a = 11 and b = 5.

**8NS2 Approximating the Values of Irrational Numbers**

Know that there are numbers that are not rational, and approximate them by rational numbers.

Example:

Approximate the value of the following irrational numbers

√3

√11

√17

**Estimating Irrational Numbers**

An instructional math video on how to make estimations about the value of irrational square roots.

An irrational number is any number that cannot be written as a fraction. Irrational numbers have decimals that keep on going forever without a repeating pattern.

How to make estimations when roots are irrational?

- Count up until you hit a square root that works.
- Count down until you hit a square root that works.
- Square root the high and low number, then graph their points on a number line.
- Your estimate should be somewhere between those two numbers.

Example:

Estimate √5 and then graph your estimate on the number line

**Estimating Square Roots**

The square root of a number n is a number whose square is equal to n, that is, a solution of the equation x^{2} =n. The positive square root of a number n, written √n, is the positive number whose square is n.

Estimate each of the following square roots

√40

√150

-√75

√75

√93

√119

√30

√45

√63

**8NS2 Estimating the Value of Irrational Expressions part 1**

Example:

Approximate the value of the following irrational number

√5

**8NS2 Estimating the Value of Irrational Expressions part 2**

Example:

Approximate the value of the following irrational number

√7

**Estimating the Value of Irrational Numbers**

A rational number is any number that can be written as a fraction: positive or negative

An irrational number is a number that cannot be written as a fraction. It is a non-repeating, non-terminating decimal.

Examples:

- Simplify the following square roots

√32

√18

√20

√75

√56

√40

√99 - Estimate the value of each irrational number

√15

√130

√2

**8.NS.2 Rational Approximations of Irrational Numbers**

Approximate square root of numbers that are not perfect squares and put them on the number line.

A number is a perfect square if you can take that many 1 × 1 unit squares and form them into a square.

When a number is a perfect square, the side length of the square it forms is called its square root.

Example:

√11 is between what two integers?

Which number in the number line below best represents the location of √122?

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