Students will be able to estimate a square root, simplify a square root, and add and multiply square roots.

Every whole number has a square root Most numbers are not perfect squares, and so their square roots are not whole numbers. Most numbers that are not perfect squares have square roots that are irrational numbers Irrational numbers can be represented by decimals that do not terminate and do not repeat The decimal approximations of whole numbers can be determined using a calculator

2 x 2 = 4 or What is a perfect Square? 2 2 A perfect square is the number that represents the area of the square. The perfect square is 4

5 5 5 x 5 = 25 The perfect square is 25. OR

The inverse of squaring a number is to take the square root of the number. Think of it as you are given the area of a square, how long is each side. The square root of 4 is 2

The square root of 16 is 4

Perfect Squares (Memorize)

By definition  25 is the number you would multiply times itself to get 25 for an answer. Because we are familiar with multiplication, we know that  25 = 5 Numbers like 25, which have whole numbers for their square roots, are called perfect squares You need to memorize at least the first 15 perfect squares

Perfect square Square root Perfect square Square root

Obj: To find the square root of a number Find the square roots of the given numbers If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth  

Obj: Estimate the square root of a number Find two consecutive whole numbers that the given square root is between Try to do this without using the table  18  115  18 is between 4 and 5  115 is between 10 and 11  16 = 4 and  25 = 5 so  100 = 10 and  121 = 11 so

Complete Text Book p 385 A. B. C.C. D.D. The tension increases as the wave speed increases

Text p The wave speed must be 9 because the square root of 81 is 9. The wave speed must be 6 because the square root of 36 is Yes -9 because (-9)(-9) is also 81. Yes -6 because (-6)(-6) is also

Text p

Steps To Simplify Radicals To SIMPLIFY means to find another expression with the same value. It does NOT mean to find the decimal approximation. Step 1: Find the LARGEST PERFECT SQUARE that will divide evenly into the number under the radical sign. That means when you divide, you get no remainders, no decimals, no fractions. Perfect square 4 8/4=2 Step 2: Write the number appearing under the radical sign as the product (multiplication) of the perfect square and your answer from dividing. Step 3: Give each number in the product its own radical sign. Step 4: Reduce the “perfect” radical that you have now created.

= 2 = 4 = 5 = 10 = 12

= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

Simplify Don’t let the number in front of the radical distract you. It is simply “along for the ride” and will be multiplied by our final answer

= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

Multiplying Radicals Step 1: Multiply the numbers under the radical and multiply the numbers outside the radical. Step 2: Simplify if possible

Multiply and then simplify

Simplify the following expressions  49 7  4-4   =-2 = =56 + 9= 65  = =25 + 7= 32

To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator