To simplify the expression √11/16 × √27/33, we can first simplify each square root separately:

√11/16 = √11 / √16 = √11 / 4

√27/33 = √27 / √33

Now, we can multiply the two simplified square roots together:

(√11 / 4) × (√27 / √33)

To multiply these fractions, we multiply the numerators together and the denominators together:

(√11 × √27) / (4 × √33)

Next, we simplify the square roots:

√11 × √27 = √(11 × 27) = √297

Therefore, the expression becomes:

√297 / (4 × √33)

Finally, we can simplify further by multiplying the square roots together:

√297 / (4 × √33) = √(297/33) / 4

Since 297/33 can be simplified to 9, the expression becomes:

√9 / 4 = 3/4

Therefore, √11/16 × √27/33 simplifies to 3/4.