Multiplying out brackets including surds - Higher
Expressions with brackets that include surds can be multiplied out or expanded.
Multiply out \((2 + \sqrt{5}) (3 + \sqrt{2})\)
Each term in the first bracket has to be multiplied by each term in the second bracket. One way to do this is to use a grid:
The four terms cannot be simplified because each of the surds has a different number inside the square root, and none of the surds can be simplified.
\((2 + \sqrt{5})(3 + \sqrt{2}) = 6 + 2\sqrt{2} + 3\sqrt{5} + \sqrt{10}\)
The same method can be used if the numbers in the surds are the same:
Simplify fully \((5 - \sqrt{3})(1 + \sqrt{3})\)
\((5 鈥 \sqrt{3}) (1 + \sqrt{3})= 5 鈥 \sqrt{3} + 5\sqrt{3} 鈥 3\)
\(= 4{\sqrt{3}} + 2\)
Question
- Expand \((7 + \sqrt{3})(8 + \sqrt{2})\)
- Expand and simplify \((4 - \sqrt{6})(3 + \sqrt{6})\)
- \(56 + 8\sqrt{3} + 7\sqrt{2} + \sqrt{6}\)
- \(12 + 4\sqrt{6} - 3\sqrt{6} 鈥 6 = 6 + \sqrt{6}\)