Remove the radical from the denominator below. Do not simplify the answer.
-2 sqrt15 / (6- sqrt13)
-2 √15 / (6- √13)
= -2 √15 / (6- √13) * (6+√13)/(6+√13)
= (-12√15 - 2√195)/(36-13)
= -(12√15 + 2√195)/23
To remove the radical from the denominator, we can use a technique called rationalizing the denominator.
To do this, we need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of the denominator is obtained by changing the sign of the radical term, so in this case, it would be (6 + sqrt13).
So, the expression becomes:
(-2 sqrt15 / (6- sqrt13)) * ((6+ sqrt13) / (6+ sqrt13))
Expanding this expression gives us:
= (-2 sqrt15 * (6+ sqrt13)) / ((6- sqrt13) * (6+ sqrt13))
Now, we can simplify the denominator using the difference of squares formula (a^2 - b^2 = (a+b)(a-b)).
The denominator becomes (6^2 - (sqrt13)^2), which simplifies to (36 - 13), and further to 23.
So, the expression becomes:
= (-2 sqrt15 * (6+ sqrt13)) / 23
Therefore, the radical has been removed from the denominator, and the final answer is (-2 sqrt15 * (6+ sqrt13)) / 23.