2\sqrt{3\sqrt{7}-1}\times \sqrt{3\sqrt{7}-1}

Let's solve the given expression step by step:

The expression is:

\[
2 \sqrt{3\sqrt{7} - 1} \times \sqrt{3\sqrt{7} - 1}
\]

### Step 1: Simplify the multiplication
Notice that we have a product of two square roots that are the same:

\[
\sqrt{3\sqrt{7} - 1} \times \sqrt{3\sqrt{7} - 1} = (\sqrt{3\sqrt{7} - 1})^2
\]

Squaring a square root eliminates the square root:

\[
(\sqrt{3\sqrt{7} - 1})^2 = 3\sqrt{7} - 1
\]

### Step 2: Multiply by 2
Now, multiply the result by 2:

\[
2 \times (3\sqrt{7} - 1) = 2 \times 3\sqrt{7} - 2 = 6\sqrt{7} - 2
\]

Thus, the simplified expression is:

\[
\boxed{6\sqrt{7} - 2}
\]

Would you like a further breakdown or have any questions?

Here are 5 related questions you might find interesting:
1. How do you simplify expressions involving square roots?
2. What happens when you square a square root?
3. Can you apply the distributive property to radical expressions?
4. How would the result change if we had \( \sqrt{a + b} \times \sqrt{a + b} \)?
5. How can you simplify \( \sqrt{a^2} \) when \( a \) is negative?

**Tip:** Always look for perfect squares when working with square roots. Squaring eliminates the root, simplifying your work.

2\sqrt{3\sqrt{7}-1} \times \sqrt{3\sqrt{7}-1}

Learn how to simplify the radical expression 2√(3√7 - 1) × √(3√7 - 1). This step-by-step solution covers square root properties and radical multiplication, making it ideal for students in Grades 9-12.

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