Surds - Higher - EduqasAdding and subtracting surds
Surds are numbers left in square root form that are used when detailed accuracy is required in a calculation. They are numbers which, when written in decimal form, would go on forever.
The rule for adding and subtracting surds is that the numbers inside the square rootThe square root of a number is a number which, when multiplied by itself, gives the original number. So the square root of 25 is 5 (5 Ă 5 = 25).must be the same.
Example
\(5 \sqrt{2} - 3 \sqrt{2} = 2 \sqrt{2}\)
This is just like collecting like terms in an expressionNumbers, symbols and operators grouped together - one half of an equation, eg 2bf + 2f + 3k..
\(4 \sqrt{2} + 3 \sqrt{3}\) cannot be added since the numbers inside the square roots, are not the same.
Question
Simplify the following surds, if possible:
\(2 \sqrt{3} + 6 \sqrt{3}\)
\(8 \sqrt{3} + 3 \sqrt{2}\)
\(2 \sqrt{5} + 9 \sqrt{5}\)
\(8 \sqrt{3}\)
Cannot add as the numbers inside the square roots are different.
\(11 \sqrt{5}\)
It may be necessary to simplify one or more surds in an expression first, before adding or subtracting the surds.