To multiply \( \sqrt{519} \) and \( \sqrt{62} \), we can use the property of square roots that states:
\[ \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \]
In this case, we have:
\[ \sqrt{519} \cdot \sqrt{62} = \sqrt{519 \cdot 62} \]
Now we just need to multiply \( 519 \) and \( 62 \):
\[ 519 \cdot 62 = 32178 \]
So, we have:
\[ \sqrt{519} \cdot \sqrt{62} = \sqrt{32178} \]
Thus, the exact answer is:
\[ \sqrt{32178} \]
This is the exact answer to the multiplication \( \sqrt{519} \cdot \sqrt{62} \). If you want to further simplify \( \sqrt{32178} \) or find its approximate value, let me know!
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