All SAT Math Resources
Example Question #11 : Exponents And Rational Numbers
Example Question #12 : Exponents And Rational Numbers
Rationalize the denominator:
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 :
Example Question #14 : Exponents And Rational Numbers
Solve for .
Example Question #15 : Exponents And Rational Numbers
Example Question #16 : 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.