Adding and subtracting surds

Surds with the same numbers under the roots can be added or subtracted

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

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

This is similar to collecting like terms in an .

\(4 \sqrt{2} + 3 \sqrt{3}\) will not simplify because the numbers inside the , are not the same.

Question

Simplify the following surds, if possible:

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

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

Step one:

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

\(=\sqrt{4} \times \sqrt{3}\)

\(= 2\sqrt{3}\)

Step two:

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

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

\(= 3\sqrt{3}\)

So, \(\sqrt{12} + \sqrt{27}\) is:

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

Simplify:

Find the exact perimeter of this shape.