holt mcdougal algebra 2 1-3 square roots 1-3 square roots warm up warm up lesson presentation lesson...

Holt McDougal Algebra 2

1-3 Square Roots1-3 Square Roots

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Holt McDougal Algebra 2

Holt McDougal Algebra 2

1-3 Square Roots

Opener-SAME SHEET-3/21Round to the nearest tenth.

1. 3.14 2. 1.97

Find each square root.

3. 4.

Write each fraction in simplest form.

5. 6.

Simplify.

7. 8.

3.1 2.0

4 25

Holt McDougal Algebra 2

1-3 Square Roots

• Graph Paper Squares

On graph paper, make squares that have sides lengths, 1-15.

Calculate the area, then find the square root

Holt McDougal Algebra 2

1-3 Square Roots

Website

Holt McDougal Algebra 2

1-3 Square Roots

Estimate square roots.

Simplify, add, subtract, multiply, and divide square roots.

Objectives

Holt McDougal Algebra 2

1-3 Square Roots

radical symbol radicand principal rootrationalize the denominatorlike radical terms

Vocabulary

Holt McDougal Algebra 2

1-3 Square Roots

The side length of a square is the square root of its area. This relationship is shown by a radical symbol . The number or expression under the radical symbol is called the radicand. The radical symbol indicates only the positive square root of a number, called the principal root. To indicate both the positive and negative square roots of a number, use the plus or minus sign (±).

or –5

Holt McDougal Algebra 2

1-3 Square Roots

Numbers such as 25 that have integer square roots are called perfect squares. Square roots of integers that are not perfect squares are irrational numbers. You can estimate the value of these square roots by comparing them with perfect squares. For example, lies between and , so it lies between 2 and 3.

Holt McDougal Algebra 2

1-3 Square Roots

Estimate to the nearest tenth.

Check On a calculator ≈ 5.1961524 ≈ 5.1 rounded to the nearest tenth.

Example 1: Estimating Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Check It Out! Example 1

Estimate to the nearest tenth.

Check On a calculator ≈ –7.4161984 ≈ –7.4 rounded to the nearest tenth.

Holt McDougal Algebra 2

1-3 Square Roots

Number Line• Place your sticky note in between the two

whole numbers.

Holt McDougal Algebra 2

1-3 Square Roots

Reteach(4-6)

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Square roots have special properties that help you simplify, multiply, and divide them.

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.

Holt McDougal Algebra 2

1-3 Square Roots

Simplify each expression. Example 2: Simplifying Square–Root Expressions

A.B.

C. D.

Holt McDougal Algebra 2

1-3 Square Roots

Check It Out! Example 2

A.

Simplify each expression.

B.

C. D.

Holt McDougal Algebra 2

1-3 Square Roots

Opener-SAME SHEET-3/22

1. Estimate to the nearest tenth. 6.7

Simplify each expression.

2.

3.

4.

5.

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square RootsI have, Who has?

Holt McDougal Algebra 2

1-3 Square Roots

If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator.

Holt McDougal Algebra 2

1-3 Square Roots

Simplify by rationalizing the denominator.

Example 3A: Rationalizing the Denominator

Holt McDougal Algebra 2

1-3 Square Roots

Square roots that have the same radicand are called like radical terms.

To add or subtract square roots, first simplify each radical term and then combine like radical terms by adding or subtracting their coefficients.

Holt McDougal Algebra 2

1-3 Square Roots

Add.

Example 4A: Adding and Subtracting Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Opener-SAME SHEET-3/25

Simplify by rationalizing each denominator.

6.

7.

8.

9.

Add or subtract.

Holt McDougal Algebra 2

1-3 Square Roots

Wkst

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Holt McDougal Algebra 2

1-3 Square Roots

Quiz