## Example Questions

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

Rationalize the denominator:       Explanation:

The conjugate of is .

Now multiply both the numerator and the denominator by and you get:  Hence we get ### Example Question #3 : How To Find A Rational Number From An Exponent

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

Solve for .       Explanation:  ### Example Question #5 : How To Find A Rational Number From An Exponent

If, What does       Explanation:

If ,

then .

### Example Question #2 : How To Find A Rational Number From An Exponent       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.

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