4.6/4.7 Squares and Square Roots/Estimating Square Roots, p192/96 Warm Up Simplify = = = = = NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer. LO: I will evaluate squares & square roots using exponents with 2 degrees of power. 6. Find the area 1.5 So √ 64 = 8 represents the principal square root; and - √ 64 = -8 represents the negative square root. THEREFORE: You can write √ 64 = ±8, which is read as “The square root of sixty-four is plus or minus eight.”

perfect between perfect  Square Roots that are between two integers are estimates.  √between is an IRRATIONAL NUMBERS.  A PERFECT SQUARE is a number that has square roots that are integers.  √ perfect is a RATIONAL NUMBER.

1.69 = ___ 2 So √1.69 = _____; therefore the window is _____ feet wide. ALWAYS use the PRINCIPAL (positive integer) square root for DISTANCE. √ 16 = The table is __ feet wide, which is less than __ feet. ___ the table _____ fit through the van door. 1. A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening? 4. The floor of a square room has an area of 256 ft². What is the perimeter of the room? 3. Ms. Estefan wants to put a fence around 3 sides of a square garden that has an area of 225 ft 2. How much fencing does she need? 2. A square window has an area of 1.69 square feet. How wide is the window? 5. A chessboard contains 32 black and 32 white squares. How many squares are along each side of the game board?

√ < √ 55 < √ √ < √ 80 < √ 7 < < 8 < < A Coast Guard boat searching for a lost sailboat covers a square area of 185 mi 2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. < < √185√___ Each side of the search area is about ____ miles long. √ 80 is between two perfect squares, therefore the √ 80 is _________________. The √ 185 is ____________ two perfect squares, therefore the √ 185 is ___________________. √ 55 is between two perfect squares, therefore the √ 55 is _________________.

HW- Day /7 Use a piece of paper to evaluate the problems on this slide.

= 12c 144c 8 = √ (12c ) 2 THINK: what number times 2 = the exponent? (c-) ² Write the monomial as a square. When evaluating monomial square roots:  Use raising a power to a power- Start with ? times 2 = the exponent  A variable raised to an ODD power uses the ABSOLUTE VALUE SYMBOL.. LO: I will evaluate the square roots of monomials using exponents with 2 degrees of power. 4.6/4.7 Day 2 Squares and Square Roots of Monomials, p192 z 6 = √ (z ) 2 = ⃒ z ⃒ THINK: what number times 2 = the exponent? (z-) ² Write the monomial as a square.

A.√ 121r 2 = THINK: (r-) ² B. √ p 8 = THINK: (p-) ² Write the monomial as a square. C. √ 81m 4 = THINK: (m-) ² Remember:  A variable raised to an even power is always positive.  A variable raised to an ODD power uses the ABSOLUTE VALUE SYMBOL. D. √ 100n 4 = E. √ 16y ¹⁴ F. √ m ² g 6 = Find the two square roots of each number. G. √ 144 = H. √ 2500 =

√x² =√x⁴ =√x⁶ = √x⁸ =√x¹⁰ =√x¹² = 1. Look for a pattern. Make a conjecture about when you do not need to use an absolute value in your answer. Think and Discuss 2. Describe what is meant by a perfect square. Give and example. 3. Explain how many square roots a positive number can have. How are these square roots different? THINK: what number times 2 = the exponent? (z-) ² Write the monomial as a square. ***Day RM p31 & 4.7 SRp199#50-59 even