Question

If $\sqrt{5}=x-2$, what is the value of $(x-2{)}^3$?

• A. $\sqrt{25}$
• B. $\sqrt{65}$
• C. $5\sqrt{5}$
• D. $2\sqrt{5}$

Answer 1

Answer: (C)

$5\sqrt{5}$

Given, $(x-2)=\sqrt{5}=5^{1/2}$.

Taking cube on both the sides, we get,

$(x-2{)}^3=(5^{\frac{1}{2}}{)}^3=5^{3/2}$

$=5\times 5^{1/2}$ $=5\sqrt{5}$.

Hence, option $C$ is correct.