PSAT Math : How to find a rational number from an exponent

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #231 : Exponents

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : How To Find A Rational Number From An Exponent

 

 

 

 

Rationalize the denominator:

Possible Answers:

Correct answer:

Explanation:

The conjugate of is  .

Now multiply both the numerator and the denominator by

and you get:

 

Hence we get

Example Question #1 : How To Find A Rational Number From An Exponent

Solve for :

Possible Answers:

Correct answer:

Explanation:

 

Example Question #3 : How To Find A Rational Number From An Exponent

Solve for .

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : How To Find A Rational Number From An Exponent

If,

 

What does

Possible Answers:

Correct answer:

Explanation:

If  ,

 then .

Example Question #5 : How To Find A Rational Number From An Exponent

Possible Answers:

Correct answer:

Explanation:

From the equation in the problem statement

Now squaring both sides we get

  this is a quadratic equation which equals

and the factors of this equation are

This gives us .

However, if we plug these solutions back into the original equation,   does not create an equality. Therefore,  is an extraneous solution.

 

Example Question #6 : How To Find A Rational Number From An Exponent

For some positive integer , if , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

If , then  must equal 3 (Note that  cannot be -3 because you need it to be positive. 

Now, plug  into the new equation :

 

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