What is the product of 8 and 8sqrt(32) in simplest radical form?

1 answer

To simplify the expression \( 8 \cdot 8\sqrt{32} \), we first calculate the product of the coefficients:

\[ 8 \cdot 8 = 64 \]

Next, we will simplify \( \sqrt{32} \). We can factor \( 32 \) as follows:

\[ 32 = 16 \cdot 2 \]

Now, we can take the square root:

\[ \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

Now we can substitute back into our expression:

\[ 8 \cdot 8\sqrt{32} = 64 \cdot \sqrt{32} = 64 \cdot 4\sqrt{2} \]

Calculating this gives:

\[ 64 \cdot 4 = 256 \]

Thus, we can express it as:

\[ 256\sqrt{2} \]

In summary, the product \( 8 \cdot 8\sqrt{32} \) in simplest radical form is:

\[ \boxed{256\sqrt{2}} \]