To simplify the expression \(\sqrt{7x} \times \sqrt{42x}\), we can use the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).
Applying this property, we get:
\[ \sqrt{7x} \times \sqrt{42x} = \sqrt{(7x) \times (42x)} \]
Now, calculate \(7 \times 42\) and \(x \times x\):
\[ 7 \times 42 = 294 \] \[ x \times x = x^2 \]
Now we combine these results:
\[ \sqrt{7x} \times \sqrt{42x} = \sqrt{294x^2} \]
Next, we can simplify \(\sqrt{294x^2}\):
Since \(x^2\) is a perfect square, we can take it out of the square root:
\[ \sqrt{294x^2} = \sqrt{294} \times \sqrt{x^2} = \sqrt{294} \times x \]
Therefore, the final simplified expression is:
\[ \sqrt{7x} \times \sqrt{42x} = x\sqrt{294} \]
Thus, the answer is:
\[ x\sqrt{294} \]
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