5.1 Multiplying and Dividing Radical Expressions
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1 Practice 5. Multiplying and Dividing Radical Expressions Multiply, if possible. Then simplify. To start, identify the index of each radical.. 4 # 6. 5 # 8. 6 # 4 9 index of both radicals is 4 # 6 Simplify. Assume all variables are positive. To start, change the radicand to factors with the necessary exponent. 4. 7x x y x y 5 = # (x ) Multiply and simplify. Assume all variables are positive. 7. # x 6 # 4 x 9. 6x 4 y # 9x 5 y Simplify each expression. Assume all variables are positive # 80. 5xy 6 # x y Error Analysis Your classmate simplified 5x # 5xy to 5x y. What mistake did she make? What is the correct answer? 4. A square rug has sides measuring 6 ft by 6 ft. What is the area of the rug?
2 Practice (continued) Multiplying and Dividing Radical Expressions Divide and simplify. Assume all variables are positive. To start, write the quotient of roots as a root of a quotient. 5. 6x6 9x x 8 y 4 5x y 7. 75x 7 y 5x 4 = 5 6x 6 9x 4 Rationalize the denominator of each quotient. Assume all variables are positive. To start, multiply the numerator and denominator by the appropriate radical expression to eliminate the radical = 6 # 9. x 0. 7x4 y 5xy. Einstein s famous formula E = mc relates energy E, mass m, and the speed of light c. Solve the formula for c. Rationalize the denominator.. The formula h = 6t is used to measure the time t it takes for an object to free fall from height h. If an object falls from a height of h = 8a 5 ft, how long did it take for the object to fall in terms of a?
3 Practice 5. Binomial Radical Expressions Simplify if possible. To start, determine if the expressions contain like radicals xy + y both radicals 4. A floor tile is made up of smaller squares. Each square measures in. on each side. Find the perimeter of the floor tile. Simplify. To start, factor each radicand = 9 # + 6 # Multiply Multiply each pair of conjugates
4 Practice (continued) Binomial Radical Expressions Rationalize each denominator. Simplify the answer = # A section of mosaic tile wall has the design shown at the right. The design is made up of equilateral triangles. Each side of the large triangle is 4 in. and each side of a small triangle is in. Find the total area of the design to the nearest tenth of an inch. Simplify. Assume that all variables are positive xy + 4xy. Error Analysis A classmate simplified the expression using the steps shown. - What mistake did your classmate make? What is the correct answer? # = - - = - - =- +. Writing Explain the first step in simplifying
5 Name: Period: Secondary Honors Practice 5. Rational Exponents Simplify each expression ( ) xy ( ) i( ) ( ) 4. xy 6 5. i 6. 5 i 45 4 a 5 a 5 Write each equation in radical form Write each expression in exponential form. 0.. x. (x). 4 4 x 5 x 9 x Simplify each number ( ) Find each product or quotient. To start, rewrite the expression using exponents. ( )( 6 ) i 5 0 Simplify each number. 5 x 0. (5). (6) (6). ( 4) x 5
6 Write each expression in simplest form. Assume all variables are positive.. ( 6x 8 ) 4 4. ( 8x 5 ) 5. x 6. Error Analysis. Explain why the following simplification is incorrect. What is the correct simplification? x 0 REVIEW 7. Expand the binomial. x + ( ) 6 8. Find the specified term of the binomial expansion. Seventh term of ( x + 7) 9
7 Practice 5.4 Solving Square Root and Other Radical Equations Solve. To start, rewrite the equation to isolate the radical.. x + - = 0. x = 0. + x - = 6 x + = Solve. 4. (x - ) = (x + ) = (6x - 5) + =- 7. The formula d = ph V relates the diameter d, in units, of a cylinder to its volume V, in cubic units, and its height h, in units. A cylindrical can has a diameter of in. and a height of 4 in. What is the volume of the can to the nearest cubic inch? 8. Writing Explain the difference between a radical equation and a polynomial equation. 9. Reasoning If you are solving 4(x + ) 4 = 7, do you need to use the absolute value to solve for x? Why or why not?
8 Practice (continued) Solving Square Root and Other Radical Equations Solve. Check for extraneous solutions. First, isolate a radical, then square each side of the equation. 0. 4x + 5 = x +. -x = x. x = x 4x + 5 = (x + ). x - 7 = x + 4. x + - x + 7 = 0 5. x = x x - 7 = x + 6. Find the solutions of x + = x. a. Are there any extraneous solutions? b. Reasoning How do you know the answer to part (a)? 7. A floor is made up of hexagon-shaped tiles. Each hexagon tile has an area of 497 cm. What is the length of each side of the hexagon? (Hint: Six equilateral triangles make one hexagon.) s s!
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