Final answer:
To find the value of (√99 - √11)², simplify the expression within the parentheses and expand it using the (a - b)² formula. The value is 44.
Step-by-step explanation:
To find the value of (√99 - √11)², we can start by simplifying the expression within the parentheses. √99 can be further simplified as √(9 × 11), which is equal to 3√11. Similarly, √11 can't be simplified any further.
Thus, (√99 - √11)² simplifies to (3√11 - √11)², which can be expanded using the formula (a - b)² = a² - 2ab + b². Applying this formula, we get 9(√11)² - 2(3√11)(√11) + (√11)².
Simplifying further, we have 9(11) - 2(3)(11) + 11. This evaluates to 99 - 66 + 11 = 44.
Learn more about Simplifying square roots