Question

\(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\)

 

Answer 1

\(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\)

\(=\left(5\sqrt{5}-2\sqrt{3}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+3\sqrt{3}\right)\)

\(=\left(3\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+2\sqrt{3}\right)\)

=45-12

=33

Answer 2

\[
(5\sqrt{5} - 2\sqrt{3} - 2\sqrt{5})(3\sqrt{5} - \sqrt{3} + 3\sqrt{3})
\]

\[
(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} - \sqrt{3} + 3\sqrt{3})
\]

\[
(3\sqrt{5} - 2\sqrt{3})(3\sqrt{5} + 2\sqrt{3})
\]
\[
(a - b)(a + b) = a^2 - b^2
\]
\[
= (3\sqrt{5})^2 - (2\sqrt{3})^2
\]
\[
= 9 \cdot 5 - 4 \cdot 3
\]
\[
= 45 - 12
\]
\[
= 33
\]