If $\sqrt{24} = 4.899$, the value of $\sqrt{\frac{8}{3}}$ is

### Concept & Formula To utilize a given square root value, manipulate the fraction under the radical by multiplying the numerator and denominator by the same number to create the known value. $$ \sqrt{\frac{a}{b}} = \sqrt{\frac{a \times k}{b \times k}} $$ ### Step-by-Step Solution Given: $\sqrt{24} = 4.899$ We need to find the value of $\sqrt{\frac{8}{3}}$. Notice that the numerator $8$ can be turned into $24$ if multiplied by $3$. Multiply both the numerator and the denominator by $3$: $\sqrt{\frac{8 \times 3}{3 \times 3}}$ Simplify the fraction inside the square root: $\sqrt{\frac{24}{9}}$ Apply the square root to the numerator and denominator separately: $\frac{\sqrt{24}}{\sqrt{9}}$ This simplifies to: $\frac{\sqrt{24}}{3}$ Substitute the given value for $\sqrt{24}$: $\frac{4.899}{3}$ Perform the division: $4.899 \div 3 = 1.633$ ### Exam Strategy & Shortcut Look for relationships immediately. $8$ and $24$ are related by a factor of $3$. Multiply the fraction by $3/3$ mentally to get $24/9$. The square root of $9$ is $3$, so you just need to divide the given value by $3$. $4.8 / 3 = 1.6$. Only option (c) matches. ### Common Pitfall Students often try to divide $8$ by $3$ to get $2.666...$ and then attempt to find the square root of $2.666...$ manually. This ignores the given information and guarantees a difficult calculation. ### Final Answer Therefore, the correct answer is **1.633**.