HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

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Presentation transcript:

HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.

In the expression, is the radical sign and 64 is the radicand. If x 2 = y then x is a square root of y. 1. Find the square root: 8 2. Find the square root: -0.2

11, Find the square root: 21 5.Find the square root: 3. Find the square root:

6.82, Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.

1 1 = = = = = = 36 49, 64, 81, 100, 121, 144,... What numbers are perfect squares?

1. Simplify Find a perfect square that goes into 147.

2. Simplify Find a perfect square that goes into 605.

Simplify

Look at these examples and try to find the pattern… How do you simplify variables in the radical? What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

Find a perfect square that goes into Simplify 5. Simplify

Simplify 1.3x 6 2.3x x 6 4.9x 18

What are Perfect Cubes? 1 3 = 1 x 1 x 1 = = 2 x 2 x 2 = = 3 x 3 x 3 = = 4 x 4 x 4 = = 5 x 5 x 5 = 125 and so on and on and on…..

2 2 2 x 2 = 4

3 x 3 = 9 3 3

4 x 4 =

5 5 5 x 5 = 25

The square root of 4 is 2

The square root of 9 is 3

The square root of 16 is 4

The square root of 25 is 5

Cubes

x 2 x 2 = 8

3 x 3 x 3 = 27

NTH ROOTS a square (second) root is written as: a cube (third) root is written as: a fourth root is written as: a fifth root is written as:

SIMPLIFY

ANSWERS xy 2

ASTRONOMY A special form of Kepler’s Third Law of Planetary Motion is given by where a is the average distance of an object from the Sun in AU (astronomical units) and P is the period of the orbit in years. If an object is orbiting the Sun with a period of 12 years, what is its distance from the Sun?

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