Adding and Subtracting Surds Flashcards

A surd is an irrational number that cannot be simplified to remove a square root (or cube root, etc.).

To simplify a surd, factorise the number under the square root into a product of a square number and another number, then simplify.

You can only add surds if they have the same radicand (the number under the square root).

You can only subtract surds if they have the same radicand (the number under the square root).

\( \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} \)

\( 3\sqrt{2} + 5\sqrt{2} = 8\sqrt{2} \)

\( 7\sqrt{3} - 2\sqrt{3} = 5\sqrt{3} \)

If the radicands are different, you cannot add or subtract the surds directly.

\( 2\sqrt{3} + 4\sqrt{5} \) cannot be simplified further because the radicands are different.

Simplify each surd first, then check if the radicands are the same to add or subtract.