Surd

Can't remove the square root (unsolvable square root)

A surd is a number that can’t be simplified to remove a square root.

A surd has an unsolvable square root

“That’s absurd! (surd) Surely you can remove a square beetroot.” (Square root). But they couldn’t remove it (can’t remove).

Examples

1. $sqrt2$ can’t be removed, therefore $sqrt2$ is a surd.

2. $sqrt4$ is equal to 2, so it can be removed, therefore $sqrt4$ is not a surd.

If you see the term surds in an exam you must write out the following.

Surds - Always think $sqrt9$

Try something you know.

As $sqrt9+sqrt9=3+3=6$

See if $sqrt9+sqrt9=2sqrt9$ also equals 6

$=2times3$ does equal 6

Therefore $sqrt9+sqrt9=2sqrt9$

$sqrt9-sqrt9=3-3=0$

$sqrt9timessqrt9=3times3=9=sqrt81=sqrt(9times9)$

$sqrt9timessqrt9=sqrt(9times9)$

$sqrt9/sqrt9=3/3=1=sqrt(9/9)$

$sqrt9/sqrt9=sqrt(9/9)$

Now you can work out any surd question.