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DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER ON THE CALCULATOR;. HOW DO WE SIMPLIFY RADICALS?. 1. simplify square roots, and 2. simplify radical expressions. If x 2 = y then x is a square root of y.
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DO NOW: SOLVE THE INEQUALITY BY FOLLOWING THE STEPS WE HAVE LEARNED OVER THE LAST TWO DAYS. THEN WE WILL GRAPH TOGETHER ON THE CALCULATOR;
HOW DO WE SIMPLIFY RADICALS? 1. simplify square roots, and 2. simplify radical expressions.
If x2 = y then x is a square rootof y. In the expression , is the radical signand64 is the radicand. 1. Find the square root: 8 2. Find the square root: -0.2
3. Find the square root: 11, -11 4. Find the square root: 21 5. Find the square root:
6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth. 6.82, -6.82
What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...
1. Simplify Find a perfect square that goes into 147.
2. Simplify Find a perfect square that goes into 605.
Simplify • . • . • . • .
How do you simplify variables in the radical? What is the answer to ? Look at these examples and try to find the pattern… As a general rule, divide the exponent by two. The remainder stays in the radical.
4. Simplify Find a perfect square that goes into 49. 5. Simplify
Simplify • 3x6 • 3x18 • 9x6 • 9x18
What are Perfect Cubes? • 13 = 1 x 1 x 1 = 1 • 23 = 2 x 2 x 2 = 8 • 33 = 3 x 3 x 3 = 27 • 43 = 4 x 4 x 4 = 64 • 53 = 5 x 5 x 5 = 125 • and so on and on and on…..
2 x 2 = 4 2 2
3 x 3 = 9 3 3
4 x 4 = 16 4 4
5 x 5 = 25 5 5
2 The square root of 4 is
3 The square root of 9 is
4 The square root of 16 is
5 The square root of 25 is
Cubes 5 6 7 8 1 2 3 4
2 x 2 x 2 = 8 2 2 2
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 1. 2. 3.
ANSWERS • 1. 7 • 2. -2 • 3. 3xy2
CUBES: Cathy is building a cubic storage room. She wants the volume of the space to be 1728 cubic feet. What should the dimensions of the cube be?
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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