Simplify $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$
A$4 + \sqrt{15}$CORRECT
B$4 - \sqrt{15}$
C$4 + \frac{\sqrt{15}}{2}$
D$\frac{8 + 2\sqrt{15}}{2}$
GCEFurther MathematicsSurds, Indices and Logarithms2020
AI
Toaster Teacher
Why the answer is A, and why the others tempt you.
Multiply numerator and denominator by the conjugate (√5 + √3): numerator = (√5 + √3)² = 5 + 2√15 + 3 = 8 + 2√15; denominator = 5 − 3 = 2. Dividing gives (8 + 2√15)/2 = 4 + √15.
Want this in Pidgin, Yoruba, Igbo or Hausa? Sign up free →
Practice more Further Mathematics questions
GCE Further Mathematics has thousands more questions like this — with Worked answers on every one.