Evaluating Algebraic Expressions 4-6Squares and Square Roots Math humor: Why wouldn’t the tree fit in the round pot? Why wouldn’t the tree fit in the round.

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Presentation transcript:

Evaluating Algebraic Expressions 4-6Squares and Square Roots Math humor: Why wouldn’t the tree fit in the round pot? Why wouldn’t the tree fit in the round pot? It had square roots.

Evaluating Algebraic Expressions 4-6Squares 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 3 2 as “three squared.” 3 3 Area = 3 2

Evaluating Algebraic Expressions 4-6Squares 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 4-6Squares 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 4-6Squares 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 4-6Squares 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) = is a square root, since = 100. –10 is also a square root, since –10 (–10) = = –7 – 49 = = = –10 – 1A. 49 1B. 100 ±7 ±10

Evaluating Algebraic Expressions 4-6Squares and Square Roots Examples: Simplify the expression. 2A. Write the monomial as a square. Use the absolute-value symbol.= 12|c| 144c 2 144c 2 = (12c) 2 2B. z6z6 z 6 = (z 3 ) 2 = |z 3 | Write the monomial as a square: z 6 = (z 3 ) 2 Use the absolute-value symbol.

Evaluating Algebraic Expressions 4-6Squares and Square Roots 2C. Write the monomial as a square. 10n 2 is nonnegative for all values of n. The absolute- value symbol is not needed. = 10n 2 100n 4 100n 4 = (10n 2 ) 2

Evaluating Algebraic Expressions 4-6Squares and Square Roots 13 2 = 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.