To solve the expression \(\sqrt{6x} \times \sqrt{42x}\), we can use the property of square roots that states:

\[
\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
\]

Thus, applying this to your expression:

\[
\sqrt{6x} \times \sqrt{42x} = \sqrt{(6x) \times (42x)} = \sqrt{252x^2}
\]

Now, simplify the square root:

\[
\sqrt{252x^2} = \sqrt{252} \times \sqrt{x^2} = \sqrt{252} \times x
\]

To simplify \(\sqrt{252}\), we can factor 252:

\[
252 = 2^2 \times 3^2 \times 7
\]

So,

\[
\sqrt{252} = \sqrt{2^2 \times 3^2 \times 7} = 2 \times 3 \times \sqrt{7} = 6\sqrt{7}
\]

Finally, the expression becomes:

\[
6x\sqrt{7}
\]

So, \(\sqrt{6x} \times \sqrt{42x} = 6x\sqrt{7}\).

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you simplify products of square roots in general?
2. What is the square root of a product of variables and constants?
3. How can you factor large numbers to simplify square roots?
4. How do square roots behave with powers of variables?
5. What are common mistakes when simplifying square root expressions?

**Tip:** When simplifying square roots, always look for perfect squares in the factorization of the number to simplify the root easily.

Learn how to simplify the expression sqrt(6x) times sqrt(42x) step by step, applying the square root multiplication rule and factorization methods. This problem is suitable for students in Grades 9-10, covering key algebraic concepts such as radicals and square root simplification.

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