To multiply square roots, you multiply the numbers inside the square root and combine any like terms outside the square root.
√11 × √7 = √(11 × 7) = √77
So, the exact answer is √77.
√11 × √7 = √(11 × 7) = √77
So, the exact answer is √77.
1. Multiply the numbers inside the square roots: 11 × 6 = 66.
2. Combine the square roots: √11 × √7 = √(11 × 7) = √77.
3. Simplify the square root (√77) if possible:
- Break down the number 77 into its prime factors: 77 = 7 × 11.
- Simplify the square root: √77 = √(7 × 11) = √7 × √11.
4. Final answer: √7 × √11.
Therefore, the exact answer is √7 × √11.
Let's calculate the given expression step by step:
First, distribute the multiplication operation:
√11 × √(6√7)
Next, simplify the expression inside the second square root:
√11 × √(6×√7) = √11 × √(6√7)
Now, simplify the expression inside the second square root further:
√11 × √(6×√7) = √11 × √(6) × √√7
Since √(6) is not a perfect square, and √√7 cannot be simplified further, this is the final answer:
√11 × √(6) × √√7
It is important to note that this is an exact answer using the given expressions. To obtain a numeric approximation, you can substitute the respective values of √11, √(6), and √√7 into a calculator.