Question

sqrt(11^2-9^2)
The answer is 2sqrt10, but I need to know how to get to that answer.

Answer 1

[\large \sqrt{11^2-9^2}\]


[\large \sqrt{121-81}\]


[\large \sqrt{40}\]


[\large \sqrt{4*10}\]


[\large \sqrt{4}*\sqrt{10}\]


[\large 2\sqrt{10}\]
So [\large \sqrt{11^2-9^2}=2\sqrt{10}\]

Answer 2

Thank you, I'm in college and haven't had an algebra class in a while, I just needed a quick reminder :)

Answer 3

\[\large11^2 = (9 + 2)^2 = 9^2 + 2(18) + 2^2\]
\[\large\implies 11^2 - 9^2 = 40\]\[\large\implies \sqrt{11^2 - 9^2} = \sqrt{40}\]\[\large=\sqrt{2^2\cdot 2 \cdot 5}\]\[\large=2\sqrt{2\cdot 5} = 2\sqrt{10}\]