Square root of 5/8
Understand the Problem
The question is asking for the square root of the fraction 5/8, which involves understanding how to calculate square roots of rational numbers.
Answer
$\frac{\sqrt{10}}{4}$
Answer for screen readers
The square root of the fraction $\frac{5}{8}$ is $\frac{\sqrt{10}}{4}$.
Steps to Solve
- Identify the square root of a fraction
To find the square root of a fraction, you can take the square root of the numerator and the denominator separately. So for the fraction $\frac{5}{8}$, we calculate: $$ \sqrt{\frac{5}{8}} = \frac{\sqrt{5}}{\sqrt{8}} $$
- Simplify the square root of the denominator
Next, we can simplify $\sqrt{8}$. We know that $8$ can be expressed as $4 \cdot 2$, and we can take the square root of $4$ out of the square root: $$ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} $$
- Substitute back in
Now we can substitute our simplification back into the equation: $$ \sqrt{\frac{5}{8}} = \frac{\sqrt{5}}{2\sqrt{2}} $$
- Rationalize the denominator
To make the denominator a rational number, multiply the numerator and the denominator by $\sqrt{2}$: $$ \frac{\sqrt{5}}{2\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{10}}{2 \cdot 2} = \frac{\sqrt{10}}{4} $$
The square root of the fraction $\frac{5}{8}$ is $\frac{\sqrt{10}}{4}$.
More Information
The square root of a fraction is an important concept in math and helps in understanding how to handle rational numbers. Simplifying square roots and rationalizing denominators are common algebraic techniques.
Tips
- Forgetting to simplify square roots before rationalizing denominators can lead to longer and more complicated expressions.
- Neglecting the simplification step of breaking down the denominator can also cause confusion.
