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Exponents Outline for Topic 5: Square Root Concept: Square Root Name: Warm Up 1. Multiply the following: (a) 22 = (b) 32 = (c) 42 = (d) 52 = (e) 62 = (f) 72 == COMPUTER COMPONENT Instructions: Select the computer program Understanding Exponents (Neufeld) Follow the instructions to the Main Menu. Select Square Root from the Main Menu. Work through all sections of this topic in order: • Squaring Numbers • Square Roots • Radical Signs • Square Roots of Negative Numbers • Examples Questions • Estimating Square Roots • Estimating Square Roots on a Number Line • Practice Questions Additional Required Materials: Scientific calculator As you work through the computer exercises, make your notes in the NOTES section of this page. When you reach the end of the section Practice Questions on the computer, move on to the OFF COMPUTER EXERCISES below. Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 1 Exponents Outline for Topic 5: Square Root NOTES Squaring Numbers A number is squared when it is ____________________ by _____________. Fill in the following examples of squares. 12 = 1 1 = 1 22 = ____ ____ = _______ (-2)2 = ____ ____ = _______ 72 = ____ ____ = _______ (-7)2 = ____ ____ = _______ 4.52 = ____ ____ = _______ (-4.5)2 = ____ ____ = _______ a2 = ____ ____ = _______ (-a)2 = ____ ____ = _______ Fill in the blanks. (a) Every positive number has ____ square roots; one _____________________ and one _______________________________. Example: Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 2 Exponents Outline for Topic 5: Square Root 22 = 2 ______ = ______ (-2)2 = ( -2 ) ( ____ ) = _____ The square roots of __________ are ________ and _______ . (b) The symbol is called a ___________________ sign. (c) The radical sign tells you to take the______________________ square root. What number has been squared to get the number under the square root symbol? (a) 64 (b) 25 A number cannot be _____________________ by __________________ to give a __________________ product. Example: -4 2 2 = 4 -2 -2 = 4 The product is always a __________________ number. We ______________________ take the square root of a _______________________ number. Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 3 Exponents Outline for Topic 5: Square Root Remember: Operations ______________ the _________________ sign are done _________. Example: 4 + 10 = ________ = ________ A square root can be written as a __________ of two radicals. Example: (a) 6 = 2 3 = ___ ___ (b) 9 = 3 3 --- = ( ) ___ When estimating square roots. First, find an easier square root that is close, but a little _____________than it. Then find an easier square root that is just a little ____________ than it. Example: (a) 28 is ____________ and Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 4 Exponents Outline for Topic 5: Square Root OFF COMPUTER EXERCISES 1. Find the square roots of each number. (a) 81 (b) 64 (c) 1 (d) 0 (e) 100 (f) 144 (g) 9 (h) 225 2. Which square roots are the following between? (a) 72 (b) 38 (c) 109 Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 5 Exponents Outline for Topic 5: Square Root 3. Fill in the missing numbers on the radical clock face: 4. Evaluate. (b) - Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 6 Exponents Outline for Topic 5: Square Root (c) (d) - (e) + (g) (h) Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 7 Exponents Outline for Topic 5: Square Root (i) (j) (k) (l) 4 + Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 8 Exponents Outline for Topic 5: Square Root 5. Evaluate each expression if x = 3, y = -4 and z = -7. (a) - (b) (c) (d) Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 9 Exponents Outline for Topic 5: Square Root 6. Answer the following and show all your steps. (a) If the area of a square is 289 square mm, calculate the dimensions. (b) If the area of a square is 0.0081 square cm, calculate the dimensions. (c) A rectangle has dimensions of 4 cm by 16 cm and is equal to a second figure which is a square. Find the dimensions of the square. Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 10 Exponents Outline for Topic 5: Square Root Challenge 6. Calculate the square root of (43 + 43 + 43 + 43). 7. Find a number x to make this statement true: 4 + ( x ÷ 42) – 2 32 = 18 Neufeld Learning Systems Inc. 2008 www.neufeldmath.com 11

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posted: | 11/11/2011 |

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