What is the √160r^2

Answer 1

To simplify \( \sqrt{160r^2} \), you can break it down into two parts:

1. Simplify \( \sqrt{160} \):

   • Factor 160 into its prime factors: \( 160 = 16 \times 10 = 16 \times 2 \times 5 = 2^4 \times 5 \).
   • The square root of \( 160 \) can be simplified: \[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \]

2. Simplify \( \sqrt{r^2} \):

   • The square root of \( r^2 \) is \( r \) (assuming \( r \) is non-negative).

Putting it all together, we have: \[ \sqrt{160r^2} = \sqrt{160} \cdot \sqrt{r^2} = 4\sqrt{10} \cdot r = 4r\sqrt{10} \]

So, the simplified form of \( \sqrt{160r^2} \) is \( 4r\sqrt{10} \).