Exploring Square Roots and the Pythagorean Theorem By: C Berg Edited By: V T Hamilton

Perfect Square

A number that is a square of an integer Ex: 3 2 = 3 · 3 = 9 3 3 Creates a Perfect Square of 9

Perfect Square

List the perfect squares for the numbers 1-12

Square Root

The inverse of the square of a number

Square Root

Indicated by the symbol Radical Sign

Square Root

Example:  4

Square Root

Estimating square roots of non-perfect squares

Square Root

Find the perfect squares immediately greater and less than the non-perfect square

Square Root

Example: The answer is between 8 2 which is 64 and 9 2 which is 81

Pythagorean Theorem

Pythagorean Theorem

Formula to find a missing side of a right triangle

Pythagorean Theorem

ONLY WORKS FOR RIGHT TRIANGLES!!!

Pythagorean Theorem

Part of a Right Triangle: •Hypotenuse •2 Legs

Pythagorean Theorem

a leg = c = hypotenuse b = leg

Pythagorean Theorem

c = hypotenuse a = leg b = leg

Pythagorean Theorem

•Lengths of the legs: a & b •Length of the hypotenuse: c

Pythagorean Theorem

The sum of the squares of the legs is equal to the square of the hypotenuse

Pythagorean Theorem

a 2 + b 2 = c 2

Pythagorean Theorem

5 2 3 2 3 4 5 4 2 3 2 + 4 2 = 5 2 9 + 16 = 25 25 = 25