Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Warm Up 11/9/2015 Who makes it, has no need of it. Who buys it, has no use for it. Who uses it can neither see nor feel it. What is it? A Coffin!!! Squares & Square Roots Perfect Squares Square Number Also called a “perfect square” A number that is the square of a whole number Can be represented by arranging objects in a square. Square Numbers Square Numbers 1x1=1 2x2=4 3x3=9 4 x 4 = 16 Square Numbers 1x1=1 2x2=4 3x3=9 4 x 4 = 16 Activity: Calculate the perfect squares up to 152… Square Numbers 1x1=1 9 x 9 = 81 2x2=4 10 x 10 = 100 3x3=9 11 x 11 = 121 4 x 4 = 16 12 x 12 = 144 5 x 5 = 25 13 x 13 = 169 6 x 6 = 36 14 x 14 = 196 7 x 7 = 49 15 x 15 = 225 8 x 8 = 64 Activity: Identify the following numbers as perfect squares or not. i. ii. iii. iv. v. vi. 16 15 21 36 64 71 Activity: Identify the following numbers as perfect squares or not. 16 = 4 x 4 ii. 15 iii. 21 iv. 36 = 6 x 6 v. 64 = 8 x 8 vi. 71 i. Squares & Square Roots Square Roots Parts of a Radical Expression Finding a root of a number is the inverse operation of raising a number to a power. radical sign index n a radicand This symbol is the radical or the radical sign The expression under the radical sign is the radicand. The index defines the root to be taken. Square Root A number which, when multiplied by itself, results in another number. Ex: 5 is the square root of 25. 5 = 25 Every positive number has two square roots, one positive and one negative When you calculate the square root of a number on a calculator, only the positive square root appears. This is the principal square root. Principal Square RootThe non-negative square root of a number. Activity: Find the principal square roots of the following numbers Warm Up 11/10/15 What gets wetter and wetter the more it dries? A towel!!! Radical Product Property a b ab ONLY when a≥0 and b≥0 For Example: 9 16 9 16 144 12 9 16 3 4 12 Equal Simplify the following expressions Simplifying Square Roots Write the following as a radical (square root) in simplest form: 36 is the biggest perfect square that divides 72. Simplify. 72 36 2 36 2 6 2 Rewrite the square root as a product of roots. 27 9 3 9 3 3 3 Ignore the 5 multiplication until the end. 5 32 5 16 2 5 16 2 5 4 2 20 2 Simplifying Square Roots Simplify these radicals: A) 16 4 B) 8 C) 7 E )4 63 12 2 2 D) 75 7 5 3 F ) 128 8 2 11/12/15 Warm up A man is pushing his car along, and when he reaches a hotel he shouts “I’m bankrupt!” Why? He’s playing Monopoly!!! Radical Quotient Property a b a b ONLY when a≥0 and b≥0 For Example: 64 16 64 16 64 16 4 2 8 4 2 Equal Simplify the expressions Simplifying Radicals using the Quotient Rule Quotient Rule for Square Roots If a and b are real numbers and b 0, then Examples: 16 4 16 81 81 9 45 49 45 49 2 25 95 3 5 7 7 2 2 5 25 a a b b The Square Root of a Fraction Write the following as a radical (square root) in simplest form: Take the square root of the numerator and the denominator 3 3 3 2 4 4 Simplify. Simplify the expressions Warm Up 11/13/15 Define the following (you can look these up on your computer if you don’t know them!): Rational Number any # that can be expressed as the quotient of 2 integers Irrational Numberany real # that cannot be expressed as a ratio of integers. What can run but never walks, has a mouth but never talks, has a bed but never sleeps? A river!!!! Rationalizing a Denominator The denominator of a fraction cannot contain a radical. To rationalize the denominator (rewriting a fraction so the bottom is a rational number) multiply by the same radical. Simplify the following expressions: 5 2 5 2 5 2 2 2 2 2 2 6 3 6 3 3 2 3 2 3 6 3 3 2 35 5 15 53 3 5 3 5 3 6 Why do we rationalize the denominator? The main reason we do this is to have a standard form in which certain kinds of answers can be written. That makes it easier for us as teachers to check answers, and for the students to check their own answers in their book. More answers at: http://mathforum.org/library/drmath/view/5 2663.html Simplify the expressions