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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.

Part of MathsNumber

Adding and subtracting surds

The rule for adding and subtracting surds is that the numbers inside the must be the same.

Example

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

This is just like collecting like terms in an .

\(4 \sqrt{2} + 3 \sqrt{3}\) cannot be added since the numbers inside the square roots, are not the same.

Question

Simplify the following surds, if possible:

  1. \(2 \sqrt{3} + 6 \sqrt{3}\)
  2. \(8 \sqrt{3} + 3 \sqrt{2}\)
  3. \(2 \sqrt{5} + 9 \sqrt{5}\)

It may be necessary to simplify one or more surds in an expression first, before adding or subtracting the surds.

Example

\(\sqrt{12} + \sqrt{27}\)

\(12 = 4 \times 3\) so \(\sqrt{12} = \sqrt{(4 \times 3)} = 2 \sqrt{3}\)

\(27 = 9 \times 3\) so \(\sqrt{27} = \sqrt{(9 \times 3)} = 3 \sqrt{3}\)

\(\sqrt{12} + \sqrt{27} = 2 \sqrt{3} + 3 \sqrt{3} = 5 \sqrt{3}\)

Question

Subtract these surds:

  1. \(\sqrt{12} - \sqrt{27}\)
  2. \(\sqrt{48} - \sqrt{12}\)

Question

zwfckqt Find the exact perimeter of this shape.