Question 1

Simplify: \(\sqrt 3 \;\left( {2 + \sqrt 6 } \right)\)

\(2\sqrt 3 + 3\sqrt 2 \)

Question 2

Simplify: \(\left( {\sqrt {45} + \sqrt {27} } \right)\;\left( {\sqrt 3 - \sqrt 2 } \right)\)

\(9 + 3\sqrt {15} - 3\sqrt {10} - 3\sqrt 6 \)

Question 3

Simplify: \({\left( {\sqrt {17} - \sqrt {13} } \right)^2}\)

\(30 - 2\sqrt {221} \)

Question 4

Simplify: \(\left( {\sqrt 6 + \sqrt {15} } \right)\;\left( {\sqrt 3 - \sqrt 2 } \right)\)

\(3\left( {\sqrt 2 + \sqrt 5 } \right) - 2\sqrt 3 - \sqrt {30} \)

Question 5

Simplify: \(\left( {6\sqrt {10} + 10\sqrt 3 } \right)\;\left( {6\sqrt 5 - 5\sqrt 6 } \right)\)

\(30\sqrt 2 \)

Question 6

Simplify \(\sqrt{5}(3-\sqrt{10})\)

\(3 \sqrt{5}- 5 \sqrt{2}\)

Question 7

Simplify \((2 \sqrt{3}+1)(3\sqrt{2}-1)\)

\(6\sqrt{6}-2\sqrt{3}+3\sqrt{2}-1\)

Question 8

Simplify \((5 \sqrt{2}+2 \sqrt{3})^2\)

\(62+20 \sqrt{6}\)

Question 9

Simplify \((\sqrt{12}+\sqrt{8})(\sqrt{3}-\sqrt{2})\)

2

Question 10

Simplify \((\sqrt{24}+\sqrt{27})(\sqrt{54}-\sqrt{12})\)

\(18+15\sqrt{2}\)