rationalize the denominator of
1/(2+5√3)
[1/(2+5sqrt3)](2-5sqrt3)/(2-5sqrt3)
=(2-5sqrt3)/(4-75)
= (5 sqrt3-2)/71
To rationalize the denominator of the fraction 1/(2+5√3), we need to get rid of the square root in the denominator. Here's how you can do it:
Step 1: Multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of 2+5√3 is 2-5√3.
1/(2+5√3) * (2-5√3)/(2-5√3)
Step 2: Simplify the denominator by multiplying using the FOIL method (First, Outer, Inner, Last).
(2 * 2) + (2 * -5√3) + (-5√3 * 2) + (-5√3 * -5√3)
4 - 10√3 - 10√3 + 75
79 - 20√3
Step 3: Rewrite the fraction using the simplified denominator.
1/(2+5√3) * (2-5√3)/(79-20√3)
So, the rationalized denominator of the fraction 1/(2+5√3) is (79 - 20√3).