Square Roots and Irrational Numbers

Square Roots and Irrational Numbers Finding square roots and identifying real numbers

Write the first 20 terms of the following sequence: 1, 4, 9, 16, … 16 100 121 144 169 196 225 256 289 324 361 400 25 36 49 x2 1 4 9 64 81 These numbers are called the Perfect Squares.

Perfect Squares • A perfect square is simply the square of each number. Ex.

Square Root • Finding the square root is the inverse of squaring a number and is denoted by the square symbol. square root symbol

You would read this as the square root of 81 Written another way, what number when multiplied by itself give you 81 = 9 So the square root of 81 is 9

Rational Numbers • A rational number is a number that can be expressed as a ratio of two numbers WHAT ON EARTH DOES THAT MEAN?

A rational number can be written as a fraction • Ex. and so on. • When written as a decimal, a rational number either terminates, or repeats. • Ex.

Irrational Numbers • An irrational number is a number that in decimal form does not terminates nor does it repeat. • An irrational number cannot be written as a fraction. • Ex. 3.87298334……., ,

Practice • Identify the following numbers as rational or irrational. .333333 Rational because 49 is a perfect square Rational because it is a terminating decimal Irrational because 3 is not a perfect square Rational because it is a repeating decimal

Practice • Identify the following numbers as rational or irrational. Irrational because it does not repeat nor does it terminate Rational because it is a terminating decimal Irrational because 15 is not perfect square

Pythagorean Theorem Using the Pythagorean theorem and identifying right triangles

Pythagorean Theorem • The legs of the right triangle are the shortest sides of the triangle • The hypotenuse of the right triangle is the longest side, and is opposite the right angle

Pythagorean Theorem • In any right triangle, the sum of the square of the lengths of the legs is equal to the square of the length of the hypotenuse Pythagorean Theorem

Using the Pythagorean Theorem, when given two sides of a right triangle, we can find the third side. • We can also use the Pythagorean Theorem when given the sides of a triangle to determine if those sides form a right triangle

Practice • The length of two sides of a triangle are given, find the length of the third side. Legs: 3 ft. and 4 ft.

Practice • The length of two sides of a triangle are given, find the length of the third side. Legs: 12ft. and 5ft.

Practice • The length of two sides of a triangle are given, find the length of the third side. Leg: 12ft. Hypotenuse: 15 ft.

Practice • Do these numbers form a right triangle?

Square Roots and Irrational Numbers