To simplify \( \sqrt{7} \times \sqrt{8} \), we can use the property of square roots that states:
\[ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \]
Applying this to our expression:
\[ \sqrt{7} \times \sqrt{8} = \sqrt{7 \times 8} \]
Calculating \( 7 \times 8 \):
\[ 7 \times 8 = 56 \]
So we have:
\[ \sqrt{7} \times \sqrt{8} = \sqrt{56} \]
Next, we can simplify \( \sqrt{56} \). First, we find the prime factorization of 56:
\[ 56 = 7 \times 8 = 7 \times 4 \times 2 = 7 \times 2^3 \]
Now, we can write \( \sqrt{56} \) as:
\[ \sqrt{56} = \sqrt{7 \times 2^3} = \sqrt{7} \times \sqrt{2^3} \]
The square root of \( 2^3 \) can be simplified:
\[ \sqrt{2^3} = \sqrt{2^2 \times 2} = \sqrt{2^2} \times \sqrt{2} = 2 \times \sqrt{2} \]
Combining this back, we have:
\[ \sqrt{56} = \sqrt{7} \times (2 \times \sqrt{2}) = 2\sqrt{7} \times \sqrt{2} \]
This can be rearranged as:
\[ 2 \sqrt{14} \]
Thus, the final answer, in exact form, is:
\[ \boxed{2\sqrt{14}} \]
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