nth root functions Quiz 1

Question 1

Statement 1: $$\sqrt[5]{{{{\left( { - 5} ight)}^5}}} =  - 5$$ $$ \ $$ Statement 2: $$\sqrt[5]{{{{\left( { - 5} ight)}^5}}} = 5$$ $$ \ $$ Statement 3: $$\sqrt[4]{{{{\left( { - 5} ight)}^4}}} = 5$$ $$ \ $$ Which of these statements is true?

Accepted Answer

$$1,\;3$$

Answer

$$1,\;2,\;3$$

Answer

$$1,\;2$$

Answer

$$2,\;3$$

Question 2

Which of the following properties is true for the $${n^{th}}$$ root of an expression?

Accepted Answer

$$\sqrt[n]{{{{\left( {\dfrac{x}{y}} \right)}^m}}} = \dfrac{{{x^{\dfrac{m}{n}}}}}{{{y^{\dfrac{m}{n}}}}}$$

Answer

$$\sqrt[n]{{{x^n}}} = x$$

Answer

$$\sqrt[n]{{x + y}} = \sqrt[n]{x} + \sqrt[n]{y}$$

Answer

$${\left( {\sqrt[n]{x}.\sqrt[n]{y}} \right)^m} = {\left( {xy} \right)^{m - n}}$$

Question 3

Solve for $$y$$ where $$81{\left( {y - \dfrac{4}{3}} \right)^{\dfrac{1}{2}}} = 27$$

Accepted Answer

$$\dfrac{{13}}{9}$$

Answer

$$\dfrac{{17}}{9}$$

Answer

$$\dfrac{{11}}{5}$$

Answer

$$\dfrac{{15}}{{13}}$$

Question 4

The domain of the function $$f\left( x \right) = \dfrac{{\left( {\sqrt {x - 2} } \right)\left( {\sqrt[3]{{x - 3}}} \right)}}{{\left( {\sqrt[4]{{x - 4}}} \right)}}$$ is

Accepted Answer

$$\left( {4,\infty } \right)$$

Answer

$$\left[ {2,\infty } \right)$$

Answer

$$\left( {3,\infty } \right)$$

Answer

$$\left( {2,\infty } \right)$$

Question 5

The graph of the function $$f\left( x \right) = \sqrt x  + \sqrt[3]{x}$$ is given as

Accepted Answer

Answer

Answer

Answer