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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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


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


1-3 Square Roots

Website


1-3 Square Roots

Estimate square roots.

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

Objectives


1-3 Square Roots

radical symbol radicand principal rootrationalize the denominatorlike radical terms

Vocabulary


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


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.


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


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.


1-3 Square Roots

Number Line• Place your sticky note in between the two

whole numbers.


1-3 Square Roots

Reteach(4-6)


1-3 Square Roots


1-3 Square Roots

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


1-3 Square Roots


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.


1-3 Square Roots

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

A.B.

C. D.


1-3 Square Roots

Check It Out! Example 2

A.

Simplify each expression.

B.

C. D.


1-3 Square Roots

Opener-SAME SHEET-3/22

1. Estimate to the nearest tenth. 6.7

Simplify each expression.

2.

3.

4.

5.


1-3 Square Roots


1-3 Square RootsI have, Who has?


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.


1-3 Square Roots

Simplify by rationalizing the denominator.

Example 3A: Rationalizing the Denominator


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.


1-3 Square Roots

Add.

Example 4A: Adding and Subtracting Square Roots


1-3 Square Roots

Opener-SAME SHEET-3/25

Simplify by rationalizing each denominator.

6.

7.

8.

9.

Add or subtract.


1-3 Square Roots

Wkst


1-3 Square Roots


1-3 Square Roots

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

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