Question

question
express in simplest radical form.
\\(\frac{\sqrt{24}}{10}\\)

Explanation:

Step1: Factor the radicand

Factor 24 into a product of a perfect square and another number: $24 = 4\times6$, where 4 is a perfect square. So, $\sqrt{24}=\sqrt{4\times6}$.

Step2: Use the property of square roots

Using the property $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (for $a\geq0, b\geq0$), we get $\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}$. Since $\sqrt{4} = 2$, this simplifies to $2\sqrt{6}$.

Step3: Substitute back and simplify the fraction

Now substitute $\sqrt{24}=2\sqrt{6}$ into the original expression $\frac{\sqrt{24}}{10}$, we get $\frac{2\sqrt{6}}{10}$. Then simplify the fraction by dividing numerator and denominator by 2: $\frac{2\sqrt{6}\div2}{10\div2}=\frac{\sqrt{6}}{5}$.

Answer:

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