What is the product of 8, square root of, 14, end square root814​ and 5, square root of, 12, end square root512​ in simplest radical form?

To find the product of \( 8\sqrt{14} \) and \( 5\sqrt{12} \):

1. First, simplify \( \sqrt{12} \):
   \[
   \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
   \]
   So, \( 5\sqrt{12} = 5 \times 2\sqrt{3} = 10\sqrt{3} \).

2. Now, multiply \( 8\sqrt{14} \) and \( 10\sqrt{3} \):
   \[
   8\sqrt{14} \times 10\sqrt{3} = (8 \times 10)(\sqrt{14} \times \sqrt{3}) = 80\sqrt{42}
   \]

Thus, the product in simplest radical form is \( 80\sqrt{42} \).

Would you like any further details or explanations? Here are some related questions you might consider:

1. How do you simplify square roots in general?
2. Can you provide another example of multiplying radicals?
3. What is the significance of simplifying radical expressions?
4. How can this method be applied to larger numbers?
5. What are some common mistakes when working with square roots? 

**Tip:** Always check if you can simplify square roots before multiplying.

What is the product of 8√14 and 5√12 in simplest radical form?

Learn how to find the product of 8√14 and 5√12 in its simplest radical form. This problem involves simplifying square roots and multiplying radicals, making it suitable for students in Grades 9-11.

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