All PSAT Math Resources
Example Question #232 : Exponents
Example Question #233 : Exponents
Rationalize the denominator:
The conjugate of is .
Now multiply both the numerator and the denominator by
and you get:
Hence we get
Example Question #11 : Exponents And Rational Numbers
Solve for :
Example Question #235 : Exponents
Solve for .
Example Question #12 : Exponents And Rational Numbers
Example Question #13 : Exponents And Rational Numbers
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 #1 : How To Find A Rational Number From An Exponent
For some positive integer , if , what is the value of ?
If , then must equal 3 (Note that cannot be -3 because you need it to be positive.
Now, plug into the new equation :