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

IslaIng said:
Sorry, am hoping it’s now attached.View attachment 36420
Click to expand...

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]?
 
IslaIng said:
Is anyone able to check this please? It is simplifying surds.

View attachment 36416
Click to expand...
IslaIng said:
Sorry, am hoping it’s now attached.View attachment 36420
Click to expand...
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. ?
 
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