Check this please? It's simplifying surds: sqrt{20} + sqrt{45} - sqrt{5}


Super Moderator
Staff member
Feb 4, 2004
Sorry, am hoping it’s now attached.View attachment 36420

Okay; you've gotten to this point:

[imath]\qquad 2\sqrt{5\;} + 3\sqrt{5\;} - \sqrt{5\;}[/imath]

This means the same thing as:

[imath]\qquad 2\sqrt{5\;} + 3\sqrt{5\;} - 1\sqrt{5\;}[/imath]

What is the value of [imath]2 + 3 - 1[/imath]?

The Highlander

Full Member
Feb 18, 2022
Is anyone able to check this please? It is simplifying surds.

View attachment 36416
Sorry, am hoping it’s now attached.View attachment 36420
Yes, it's correct as far as you have gone, but it should be further simplified.

As has already been alluded to, you are showing addition & subtraction of like terms in your final line.

If you have 2 apples plus 3 oranges minus 1 lemon, that cannot be simplified any further. (You can't add apples to oranges).

But what if you have 2 bananas plus 3 bananas minus 1 banana? That can give a single result can't it?
(And what if a banana was the 'equivalent' of
\(\displaystyle \sqrt{5}\) ?)

You should then arrive at a final answer in the form of
\(\displaystyle x\sqrt{y}\) (my preferred form) or simply \(\displaystyle \sqrt{z}\) if you preferred.

Hope that helps.