SAT II Math I : Irrational Numbers

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

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Example Question #5 : Irrational Numbers

Which of the following is not an irrational number?

Possible Answers:

Correct answer:

Explanation:

A root of an integer is one of two things, an integer or an irrational number. By testing all five on a calculator, only  comes up an exact integer - 5. This is the correct choice.

Example Question #1 : Irrational Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the conjugate of the denominator, which is . Then take advantage of the distributive properties and the difference of squares pattern:

Example Question #6 : Number Theory

Possible Answers:

Correct answer:

Explanation:

Example Question #7 : Number Theory

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL technique:

Example Question #2 : Irrational Numbers

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

We can set  in the cube of a binomial pattern:

Example Question #8 : Number Theory

Evaluate 

Possible Answers:

You cannot divide by complex numbers

Correct answer:

Explanation:

To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem,  is our denominator, so we will multiply the expression by  to obtain:

.

We can then combine like terms and rewrite all  terms as . Therefore, the expression becomes:

Our final answer is therefore 

Example Question #2 : Imaginary Roots Of Negative Numbers

Simplify the following product:

Possible Answers:

Correct answer:

Explanation:

Multiply these complex numbers out in the typical way:

and recall that  by definition. Then, grouping like terms we get

which is our final answer.

Example Question #1 : Irrational Numbers

Identify the real part of

Possible Answers:

none of the above.

Correct answer:

Explanation:

A complex number in its standard form is of the form: , where  stands for the real part and  stands for the imaginary part. The symbol  stands for .

The real part in this problem is 1.

Example Question #4 : Irrational Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

Example Question #5 : Irrational Numbers

Simplify:

Possible Answers:

Correct answer:

Explanation:

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in  for 

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