Final answer:
The product of 2 √7 and 10 √21 is found by multiplying the coefficients and combining the radicals, simplifying 20×√147 to 140√3, which is not listed among the and given choices. There may be an error in the options provided.
Step-by-step explanation:
To find the product of 2 √7 and 10 √21 in simplest radical form, you first multiply the coefficients (2 and 10), and then multiply the radicals (√7 and √21). Multiplying the coefficients gives us 2 × 10 = 20. Next, to multiply the radicals, you can combine them under a single radical sign: √7 × √21 = √(7 × 21).
Calculating the product inside the radical gives us √(7 × 21) = √147. Therefore, the product in simplest radical form is 20× √147. However, we can simplify the radical √147 further because 147 has a square factor of 49 (7× 7). Breaking down √147 into √49 × √3 and taking the square root of 49 gives us 7√3.
Finally, our simplified answer is 20 × 7 √3, which is 140 √3. However, this does not match any of the options provided in the question. There is likely an error in the options given. If these were correct, the closest option would be 20 √147, but the radical is not in its simplest form.