Simplify the expression. \[ (\sqrt{35})(\sqrt{42}) \]

To simplify the expression \((\sqrt{35})(\sqrt{42})\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). So, we have: \[ (\sqrt{35})(\sqrt{42}) = \sqrt{35 \cdot 42} \] Now, let's calculate \(35 \cdot 42\): \[ 35 \cdot 42 = 1470 \] Thus, the expression simplifies to: \[ \sqrt{35 \cdot 42} = \sqrt{1470} \] Next, we can simplify \(\sqrt{1470}\) by factoring \(1470\). The prime factorization of \(1470\) is: \[ 1470 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 7 = 2 \cdot 3 \cdot 5 \cdot 7^2 \] This allows us to simplify \(\sqrt{1470}\): \[ \sqrt{1470} = \sqrt{2 \cdot 3 \cdot 5 \cdot 7^2} = 7\sqrt{30} \] Therefore, the simplified expression is: \[ \sqrt{35} \cdot \sqrt{42} = 7\sqrt{30} \]