Question

Simplify :

$\sqrt{24}÷\sqrt{200}$

• A. $\frac{{}^6\sqrt{27}}{5}$
• B. $\frac{{}^6\sqrt{49}}{5}$
• C. $\frac{{}^6\sqrt{81}}{5}$
• D. $\frac{{}^4\sqrt{27}}{5}$

Answer 1

Answer: (A)

$\frac{{}^6\sqrt{27}}{5}$

$24=3\times (2{)}^3$

$200=(5{)}^2\times 2^3$

$\frac{24}{200}=\frac{3\times (2{)}^3}{(5{)}^2\times 2^3}$

$\frac{24}{200}=\frac{3}{5^2}$

now taking square root on both sides

$\sqrt{\frac{24}{200}}=\frac{\sqrt{3}}{5}$

now,

${}^6\sqrt{27}$

${=}^6\sqrt{3^3}$

$=3^{\frac{3}{6}}$

$=3^{\frac{1}{2}}$

$=\sqrt{3}$

so,

$\sqrt{\frac{24}{200}}=\frac{{}^6\sqrt{27}}{5}$