Simplify: √160r^2 +√71r^4 +√100r^8

Answer 1

To simplify the expression \( \sqrt{160r^2} + \sqrt{71r^4} + \sqrt{100r^8} \), we simplify each term individually.

1. Simplifying \( \sqrt{160r^2} \): \[ \sqrt{160r^2} = \sqrt{160} \cdot \sqrt{r^2} = \sqrt{16 \cdot 10} \cdot r = 4\sqrt{10} \cdot r = 4r\sqrt{10} \]

2. Simplifying \( \sqrt{71r^4} \): \[ \sqrt{71r^4} = \sqrt{71} \cdot \sqrt{r^4} = \sqrt{71} \cdot r^2 \]

3. Simplifying \( \sqrt{100r^8} \): \[ \sqrt{100r^8} = \sqrt{100} \cdot \sqrt{r^8} = 10 \cdot r^4 \]

Now, we can combine the simplified terms: \[ \sqrt{160r^2} + \sqrt{71r^4} + \sqrt{100r^8} = 4r\sqrt{10} + r^2\sqrt{71} + 10r^4 \]

Therefore, the final simplified expression is: \[ \boxed{4r\sqrt{10} + r^2\sqrt{71} + 10r^4} \]