Square Roots and the Pythagorean Theorem

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Presentation transcript:

Square Roots and the Pythagorean Theorem Section 6.4 Square Roots and the Pythagorean Theorem

nth Root

Square Root Index is ALWAYS 2 The square root of a positive number a is the positive number b whose square is a. In symbols

Square Root Steps Write the radicand in prime factorization. Group like prime numbers in sets of two (index) One whole set becomes on prime number outside the radical symbol Multiply all numbers on the outside together Multiply all numbers on the inside together

Examples Simplify

Examples Simplify

Examples Simplify

Examples Simplify

Examples Simplify

Pythagorean Theorem Given a right triangle the hypotenuse squared is equal to the sum of each leg squared.

Example Find the missing leg

Example Find the hypotenuse

Example Find the hypotenuse

Example Find the height of the antenna. Round the height to the tenth place.