4√10 divided by √2

Answer 1

To simplify \( \frac{4\sqrt{10}}{\sqrt{2}} \), you can follow these steps:

1. Rewrite the expression by multiplying the numerator and the denominator by \( \sqrt{2} \) to eliminate the square root in the denominator:

\[ \frac{4\sqrt{10}}{\sqrt{2}} = \frac{4\sqrt{10} \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} \]

2. The denominator simplifies as follows:

\[ \sqrt{2} \cdot \sqrt{2} = 2 \]

3. In the numerator, you have:

\[ 4\sqrt{10} \cdot \sqrt{2} = 4\sqrt{20} \]

4. Thus, the expression simplifies to:

\[ \frac{4\sqrt{20}}{2} \]

5. Now simplify \( \frac{4}{2} \):

\[ \frac{4\sqrt{20}}{2} = 2\sqrt{20} \]

6. Finally, you can simplify \( \sqrt{20} \):

\[ \sqrt{20} = \sqrt{4 \cdot 5} = 2\sqrt{5} \]

7. Therefore:

\[ 2\sqrt{20} = 2 \cdot 2\sqrt{5} = 4\sqrt{5} \]

So, the final result of \( \frac{4\sqrt{10}}{\sqrt{2}} \) is:

\[ \boxed{4\sqrt{5}} \]