Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Math humor:Math humor:

Why wouldn’t the tree fit in Why wouldn’t the tree fit in the round pot?the round pot?

It had square roots.It had square roots.

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

The square root of a number is one of the two equal factors of that number. Squaring a nonnegative number and finding the square root of that number are inverse operations.

Because the area of a square can be expressed using an exponent of 2, a number with an exponent of 2 is said to be squared. You read 32 as “three squared.”

3

3

Area = 32

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Positive real numbers have two square roots, one positive and one negative.

The positive square root, or principle square root, is represented by .

The negative square root is represented by - .

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

A perfect square is a number whose square roots are integers. {you should memorize the perfect squares below}

The first 11 perfect squares are below in the table.

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

You can write the square roots of 16 as ±4, which is read as “plus or minus four.”

Writing Math

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Example:

Find the two square roots of each number.

7 is a square root, since 7 • 7 = 49.

–7 is also a square root, since –7 • (–7) = 49.

10 is a square root, since 10 • 10 = 100.

–10 is also a square root, since –10 • (–10) = 100.

49 = –7–

49 = 7

100 = 10

100 = –10–

1A. 49

1B. 100±7

±10

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

Examples:

Simplify the expression.

2A.

Write the monomial as a square.

Use the absolute-value symbol.= 12|c|

144c2

144c2 = (12c)2

2B. z6

z6 = (z3)2

= |z3|

Write the monomial as a square: z6 = (z3)2

Use the absolute-value symbol.

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

2C.

Write the monomial as a square.

10n2 is nonnegative for all values of n. The absolute-value symbol is not needed.

= 10n2

100n4

100n4 = (10n2)2

Evaluating Algebraic Expressions

4-6 Squares and Square Roots

132 = 169

The window is 13 inches wide.

Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning.

Talking Example: Application

A square window has an area of 169 square inches. How wide is the window?

So 169 = 13.