Question

The result of $(3+\sqrt{5})\times$, is a rational number.

• A. $\sqrt{5}$
• B. 3
• C. $(3+\sqrt{5})$
• D. $(3-\sqrt{5})$

Answer 1

The correct option is D $(3-\sqrt{5})$

To convert an irrational number to a rational number, we must rationalise it.
To rationalise $(a+\sqrt{b})$, we must multiply it with $(a-\sqrt{b})$.
Similarly, to rationalise $(3+\sqrt{5})$, we must multiply it with $(3-\sqrt{5})$.
So, $(3+\sqrt{5})\times (3-\sqrt{5})=3^2-{\sqrt{5}}^2$
$=9-5=4$
which is a rational number.