Question

The value if ${(\sqrt[6]{627}-\sqrt{6\frac{3}{4}})}^2$ equals ____.

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{3}{2}$
• C. $\frac{\sqrt{3}}{4}$
• D. $\frac{3}{4}$

Answer 1

Answer: (D)

$\frac{3}{4}$

We have, $(\sqrt[6]{627}-\sqrt[2]{26\frac{3}{4}}{)}^2$

Above can be written as given,

$(\sqrt[6]{63^3}-\sqrt[2]{2\frac{27}{4}}{)}^2$

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

$=3+\frac{3^3}{4}-9=\frac{3}{4}$