Final answer:
To multiply and simplify 4 √11 * 4 √10, multiply the coefficients (16) and then multiply the square roots to get the final answer of 16√110, which cannot be further simplified.
Step-by-step explanation:
The student has asked to multiply and simplify the expression 4 √11 * 4 √10. To solve, we multiply the coefficients (4 and 4) and the square roots separately. Multiplying the coefficients gives us 16. To multiply square roots, we multiply the numbers under the radicals (in this case 11 and 10) and take the square root of the product. So, we have √(11*10) which simplifies to √110. Since 110 is not a perfect square, we cannot simplify the square root any further. Combining the coefficient and the square root gives us an answer of 16√110.
To multiply and simplify 4 √11 * 4 √10, you can use the property of radicals that states √a * √b = √(a * b). Start by multiplying the numbers outside the radicals together, which gives you 4 * 4 = 16. Then, multiply the numbers inside the radicals, which gives you √11 * √10 = √(11 * 10) = √110. Combine these results to get 16 √110. This is the simplified form of the expression.