9-2 Investigating Properties of Square Roots notes
9-2 Investigating Properties of Square Roots notes
9-2 Investigating Properties of Square Roots notes
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Mrs. Aitken’s Integrated 1 MathUnit 9 Reasoning and Measurement9-2 <strong>Investigating</strong> <strong>Properties</strong> <strong>of</strong> <strong>Square</strong> <strong>Roots</strong>Warm-upFind each square1. √81 92. √26 5.103. √17 4.124. √40 6.325. √1600 409-2 <strong>Investigating</strong> <strong>Properties</strong> <strong>of</strong> <strong>Square</strong> <strong>Roots</strong>Key term• Radical form – an expression for the value <strong>of</strong> the square root <strong>of</strong> anumber that contains the √ (radical) symbol. For example, the radicalform √75 can be simplified to 5√3.Simplifying and multiplying square rootsProduct properties <strong>of</strong> square rootsFor nonnegative numbers a and b:ab = a • ba• b = abExample:39 = 13 • 313 • 3 = 39a• a = a3• 3 = 3Example 1Simplifya. 98 b. 48 c. 50Solution 148 = 4•12a.98 = 49•2= 49 • 2= 7 2b.= 4•12= 2 12= 2 4•3= 2•2 3c.50 = 25•2= 25 • 2= 5 2= 4 39-2 <strong>Investigating</strong> <strong>Properties</strong> <strong>of</strong> <strong>Square</strong> <strong>Roots</strong>
Mrs. Aitken’s Integrated 1 MathUnit 9 Reasoning and MeasurementExample 2Simplifya. 2 3• 7 6b. 32 • 2 2Solution 2a.2 3•7 62• 7• 3• 6 ←Group radicals14•1814• 9•214• 3•242 2b.32 • 2 22 32•22 32 • 2 ←Group Radicals2•642•816Solving equations like 2x 2 = 36To solve, first get the x 2 -term by itself on one side <strong>of</strong> the equation. Keep in mind that suchequations will have two solutions, one positive and one negative, although only thepositive solution may make sense in the given situation.Example 3Solvea. 7x 2 = 525 b. 5x 2 = 315Solution 327x= 52527x525=7 72a. x = 75x =±x =±7525 • 3x =± 5 325x= 31525x315=5 52b. x = 63x =±x =±639•7x =± 3 79-2 <strong>Investigating</strong> <strong>Properties</strong> <strong>of</strong> <strong>Square</strong> <strong>Roots</strong>
Mrs. Aitken’s Integrated 1 MathUnit 9 Reasoning and MeasurementWhen finding a length, do not worry about the negative answer because length cannot benegative.Example 4The perimeter <strong>of</strong> a rectangle is 44 feet. Its width is 10 feet. Find y, the length<strong>of</strong> the diagonal.Solution 4Find the length <strong>of</strong> the rectangle.2x + 20 = 442x = 24x = 12y10Now, find the length <strong>of</strong> the diagonal.y 2 = 10 2 + 12 2y 2 = 100 + 144y 2 = 244y = √244y = √4 · √61y = 2√6112y10Example 5Find the length <strong>of</strong> the diagonal <strong>of</strong> the rectangle in terms <strong>of</strong> x.SolutionUse the Pythagorean Theorem to find y.2 2 2(6 x) + (8 x)= y2 2 236x + 64x = y2 2100x= y100x=y2 2100 •2x = y10x= yy = 10x8xy6x9-2 <strong>Investigating</strong> <strong>Properties</strong> <strong>of</strong> <strong>Square</strong> <strong>Roots</strong>
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