2.8 Review

  1. Identify all the sets of numbers that the following numbers belong to, then write the numbers from the largest set to the smallest set.

    a) -\frac{4}{7}

     

    		 b) –9.0

     

    		 c) \sqrt{8}

     

    		 d) 3.45956842…

     
  2. Evaluate the following roots using a calculator. Round your answers to the nearest tenth.

    a) \sqrt{26} b) 5\sqrt{30} c)  \sqrt[3]{58} d)  \sqrt[5]{852}
  3. Convert the following radicals into mixed radicals in simplest form.

    a) \sqrt{135}

     

     

     

     

    		 b) –3\sqrt{112}

     

     

     

     

    		 c) \frac{5}{2}\sqrt[3]{-64}

     

     

     

     

    		 d) -\frac{3}{4}\sqrt{52}

     

     

     

     
    e) 2\sqrt{144}

     

     

     

     

    		 f) \sqrt{36{a}^{6}}

     

     

     

     

    		 g) \sqrt{98{x}^{2}{y}^{7}}

     

     

     

     

    		 h)  4\sqrt{72{m}^{8}{n}^{9}}

     

     

     

     
  4. Find of the area of the right-angle triangle below, and write it in simplest radical form.

    Right angled triangle with hypotenuse of 20 cm and base of 14 cm
  5. Simplify.

    a) (2x8)(x12)

     

     

    		 b) (15m9) ÷ (–5m3)

     

     

    		 c) -\frac{2}{5}x2 • (–10x)

     

     
    d) \frac{-36x^3 y^2}{9x^2y^2}

     

     

     

    		 e) \frac{-14x y^3}{-7y}

     

     

     
  6. a) Find the simplified expression for the area of one of the faces of the cube.
    b) Find the simplified expression for the volume of the cube.

    Cube with side lengths measuring (3/2) x to the power of 3 and y to the power of 5.
  7. Simplify.

    a) \frac{-9{x}^{3}{y}^{6}}{2{x}^{2}{y}^{3}} × \frac{8{x}^{7}{y}^{4}}{-6{x}^{3}{y}}

     

     

     

     

     

     

    		 b) \frac{3{a}^{4}{b}^{2}}{9{a}^{3}{b}^{4}}

     

     

     

     

     

     

    		 c) \left(\frac{-4w^3s^4 \bullet 2ws^3}{6w^5}\right)^2

     

     

     

     

     

     
    d) (2xy)3 • (3x2y)2 • (5xy)0

     

     

     

     

     

     

     

    		 e) \frac{(-10h^4k^3)^3}{{(5hk^4)^2}{(-12h^2k)}}

     

     

     

     

     

     

     

    		 f) \frac{(4ab^2c^3)^3}{(-2a^3b^2c)^4} × \frac{1}{(a^3b^4)^3}

     

     

     

     

     

     

     
  8. Simplify. Write your answers with positive exponents.

    a) \left(\frac{p^{2}}{r^{4}}\right)^{-3}

     

     

     

     

    		 b) \left(\frac{-12x^{-3}}{6y^{-8}}\right)^{-1}

     

     

     

     

    		 c) \left(\frac{-x^3}{y}\right)^2 ÷ \left(\frac{y^3}{x^5}\right)^2

     

     

     

     
  9. Simplify.
    (i) Write your answers with positive exponents.
    (ii) Write your answers in radical form for part b.

    a) (4x^{\frac{4}{5}})(3x^{\frac{6}{5}})

     

     

     

    		 b) (8a^{\frac{1}{2}})^{\frac{4}{3}}

     

     

     

    		 c) (5x^{\frac{6}{12}})(-25x^{\frac{6}{12}})

     

     

     

Answers

1.

a) R, Q b) R, Q, I c) R, \overline{Q} d) R, \overline{Q}
2.

a) 5.1 b) 27.4 c) 3.9 d) 3.9
3.

a) 3\sqrt{15} b) –12\sqrt{7} c) –10 d) -\frac{3}{2}\sqrt{13}
e) 24 f) 6a3 g) 7xy3\sqrt{2y} h) 24m4n4\sqrt{2n}

4.  14\sqrt{51} cm2

5.

a) 2x20 b) -3m6 c) 4x3
d) –4x e) 2xy2
6.

a) \frac{9}{4}x6y10 b) \frac{27}{8}x9y15
7.

a) 6x5y6 b) \frac{a}{3b^2} c) \frac{16s^{14}}{9w^2}
d) 72x7y5 e) \frac{10h^8}{3} f) \frac{4c^5}{a^{18}b^{14}}
8.

a) \frac{r^{12}}{p^{6}}} b) \frac{-x^{3}}{2y^{8}}} c) \frac{x^{16}}{{y}^8}
9.

a) (i) 12x^{2}

 

 b) (i) 16a^{\frac{2}{3}}

(ii) 16\sqrt[3]{a^2}

 c) (i) -125x

 

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Math 10C Workbook Copyright © 2026 by Leanne Thompson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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