What is the product of the following in simplest radical form eight radical five times three radical 32

Answer 1

To simplify the expression \( 8\sqrt{5} \times 3\sqrt{32} \), we can follow these steps:

1. Multiply the coefficients (numbers outside the radical): \[ 8 \times 3 = 24 \]

2. Multiply the radicals: \[ \sqrt{5} \times \sqrt{32} = \sqrt{5 \times 32} = \sqrt{160} \]

3. Now, combine the results: \[ 24\sqrt{160} \]

4. Next, we simplify \(\sqrt{160}\). First, we factor \(160\): \[ 160 = 16 \times 10 = 16 \times 2 \times 5 = 4^2 \times 2 \times 5 \]

5. Therefore: \[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4\sqrt{10} \]

6. Substitute \(\sqrt{160}\) back into the expression: \[ 24\sqrt{160} = 24 \times 4\sqrt{10} = 96\sqrt{10} \]

So, the product of \( 8\sqrt{5} \times 3\sqrt{32} \) in simplest radical form is: \[ \boxed{96\sqrt{10}} \]