To simplify the expression \(\sqrt{6x^2} \times \sqrt{42x}\), follow these steps:

1. **Use the property of square roots**: \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).

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

2. **Multiply the terms inside the square root**:

\[
6x^2 \times 42x = 252x^3
\]

3. **Simplify the square root**:

\[
\sqrt{252x^3}
\]

4. **Factor the expression**:

\[
\sqrt{252x^3} = \sqrt{36 \times 7 \times x^2 \times x} = \sqrt{36x^2 \times 7x}
\]

5. **Take the square root of the perfect squares**:

\[
\sqrt{36x^2 \times 7x} = 6x \sqrt{7x}
\]

So, the simplified expression is:

\[
6x\sqrt{7x}
\]

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. How would the result change if there were negative exponents involved?
2. Can you simplify \(\sqrt{12x^4} \times \sqrt{18x^2}\)?
3. What are the rules for multiplying square roots with fractional exponents?
4. How do you simplify expressions involving cube roots instead of square roots?
5. What happens if you multiply square roots of different variables?

**Tip:** When simplifying square roots, always look for perfect squares that can be factored out!

Discover how to simplify the radical expression sqrt 6x^2 times sqrt 42x using properties of square roots and factoring techniques. Learn the step-by-step method to arrive at the simplified form 6x√7x, ideal for students in Grades 8-10.

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