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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5121 : Algebra Ii

Which of the below is a rational number?

Possible Answers:

$\sqrt{225}$

$\sqrt{8}$

$5-2\pi$

$\sqrt{117}$

Correct answer:

$\sqrt{225}$

Explanation:

$\sqrt{225}\ when\ simplified\ becomes\ 15\ which\ is\ a\ rational\ number.$

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Example Question #5122 : Algebra Ii

$5-\sqrt{2}\ multipled\ by\ which\ of\ the\ below\ will\ produce\ a\ rational\ number?$

Possible Answers:

$\sqrt{5-\sqrt{2}}$

$5-\sqrt{2}$

$\sqrt{2}$

$5+\sqrt{2}$

Correct answer:

$5+\sqrt{2}$

Explanation:

$An\ irrational\ binomial\ must\ be\ multiplied\ by\ its'\ complex\ conjugate\ in\ order\ to\ produce\ a\ rational\ number.$

$The\ complex\ conjugate\ for\ 5-\sqrt{2}\ is\ 5+\sqrt{2}$

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Example Question #68 : Number Theory

Which of the following is an irrational number?

Possible Answers:

sin(270)

3.14159

$\sqrt8$

$\sqrt{169}$

$i^{50}$

Correct answer:

$\sqrt8$

Explanation:

Irrational numbers cannot be expressed as a ratio of two numbers. They can be decimal numbers that go on forever without repeating.

Do not mix fixed numbers with symbolic values such as 3.14159 and $\pi$ .

The value of the sine angle sin(270) is , which is not irrational.

Square root numbers and complex numbers might not necessary be irrational after their simplified form.

$i^{50}= (i^2)^{25} = (-1)^{25} = -1$

$\sqrt8 = 2\sqrt2$

The correct answer is: $\sqrt8$

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Example Question #69 : Number Theory

Which of the following numbers are irrational?

Possible Answers:

$\sqrt6$

3.14159

$\50\%$

$\sqrt[3]{8}$

$\frac{199}{100}$

Correct answer:

$\sqrt6$

Explanation:

Irrational numbers are numbers that cannot be rewritten as a fraction of two numbers.

Be careful with numbers that may look as though they are irrational, such as 3.14159 , but is rational since this number is finite and can be expressed as a fraction.

Irrational numbers cannot include continuous numbers such as $\pi$ , and some radical numbers such as $\sqrt2$ .

Some of the radicals in the answers are not fully simplified.

The term $\sqrt[3]{8}$ can be simplified to a whole number two, which means that this is a rational number.

The correct answer is: $\sqrt6$

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Example Question #5123 : Algebra Ii

Which of the below is NOT an irrational number?

Possible Answers:

$\sqrt{12}-3$

$\sqrt{16}-\sqrt{49}$

$10-\pi$

$\sqrt{-5}$

Correct answer:

$\sqrt{16}-\sqrt{49}$

Explanation:

The correct choice involves two perfect squares which makes each number a rational number:

$\sqrt{16}-\sqrt{49}=4-7=-3\ which\ is\ a\ rational\ number$

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Example Question #32 : Irrational Numbers

Which of the following is an irrational number?

Possible Answers:

3.14159

$\sqrt{-3}$

$\sqrt{11}$

$1.6\%$

Correct answer:

$\sqrt{11}$

Explanation:

An irrational number is a number that cannot be rewritten as a ratio of two numbers such as $\pi$ or since their decimal numbers are continuous.

Square roots that are not perfect squares are irrational such as:

$\sqrt2, \sqrt5, \sqrt{11}$

Be careful with numbers that are fixed. Fixed numbers are finite and can be rewritten as a fractional term.

Imaginary numbers are neither irrational or real numbers and is defined as the term . The value of $\sqrt{-3}= i\sqrt3$ is an imaginary number. These are called complex numbers.

Percentages can be rewritten as a fraction.

The answer is: $\sqrt{11}$

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Example Question #5124 : Algebra Ii

Try without a calculator.

True or false: the set

$\left \{ \sqrt {15}, \sqrt {16} , \sqrt {17}, \sqrt {18},\sqrt {19} \right \}$

comprises only irrational numbers.

Possible Answers:

False

True

Correct answer:

False

Explanation:

The square root of an integer is rational if and only if the integer is a perfect square of another integer.

$16 = 4 \times 4 = 4 ^{2}$ ,

so 16 is a perfect square, and $\sqrt{16}$ is a rational number. The statement is therefore false.

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Example Question #5125 : Algebra Ii

Try without a calculator.

True or false: the set

$\left \{ 7 \pi , 8 \pi, 9 \pi, 10 \pi, 11 \pi \right \}$

comprises only irrational numbers.

Possible Answers:

False

True

Correct answer:

True

Explanation:

$\pi$ is an irrational number, as is any integer multiple of $\pi$ . All of the elements are integer multiples of $\pi$ , so all of them are irrational.

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Example Question #5126 : Algebra Ii

Try without a calculator.

True or false: the set

$\left \{ 5e, 6e, 7e, 8e, 9e \right \}$

comprises only irrational numbers.

Possible Answers:

True

False

Correct answer:

True

Explanation:

is an irrational number, as is any integer multiple of . All of the elements are integer multiples of , so all of them are irrational.

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Example Question #75 : Number Theory

Which of the following represents an irrational number?

Possible Answers:

$-\sqrt{144}$

$0.\overline{3}$

$-\frac{1}{1000}$

None of the numbers is irrational.

$\sqrt{26}$

Correct answer:

$\sqrt{26}$

Explanation:

First, recall the definition of irrational numbers. Irrational numbers cannot be expressed as a ratio of integers.

The answer $0.\overline{3}$ is incorrect because it is a repeating decimal that can be rewritten as the following fraction:

$\frac{1}{3}$

In a similar vein, the following choice is already written as a simple fraction (negative numbers are not irrational):

$-\frac{1}{1000}$

It is important to note that not all square roots are irrational. For instance, the following square root can be simplified quite easily:

$-\sqrt{144} = -12$

The only answer that cannot be expressed as a simple fraction is:

$\sqrt{26}=5.09901951359278449161$

The answer is:

$\sqrt{26}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #5121 : Algebra Ii

Example Question #5122 : Algebra Ii

Example Question #68 : Number Theory

Example Question #69 : Number Theory

Example Question #5123 : Algebra Ii

Which of the below is NOT an irrational number?

Example Question #32 : Irrational Numbers

Example Question #5124 : Algebra Ii

Example Question #5125 : Algebra Ii

Example Question #5126 : Algebra Ii

Example Question #75 : Number Theory

All Algebra II Resources

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