Explain this surds answer

Can anyone explain what's going on here?

Adding the image after the fact because this website is so *****ily designed it hides 90% of post functionality until after you've posted:

Specifically 11(5+sqrt(3))/22 on the last line - shouldn't it be 11/22 to end up with the final solution? Why are we suddenly doing 22/11?

Adding the image after the fact because this website is so *****ily designed it hides 90% of post functionality until after you've posted:

Specifically 11(5+sqrt(3))/22 on the last line - shouldn't it be 11/22 to end up with the final solution? Why are we suddenly doing 22/11?

So they've just done 2 steps in 1.
First they multiplied out 11(5+root3) to make 55 + 11root3
Then they divided everything by 11 to get (5 + root3) /2

Why would you multiply out a bracket when we are simplying?

Simplest form means we need to divide the numerator and denominator by their HCF which is 11 in this case.

Can anyone explain this one? Specifically why/how -2 sqrt(4) sqrt(2) on the third becomes -4 sqrt(2) on the fourth line? I get that the sqrt(4) becomes 2 but apart from that it makes no sense to me. If we're multiplying the -2 coefficient by 2 and sqrt(2), why do we do this randomly here when nothing else is being multiplied and we've already multiplied out the brackets earlier?

I mean thats just how it simplifies, because otherwise you wouldn't be able to only have root 2s and numbers, you would have a root 4 which is not the format the question wants

So `-2 + 2(sqrt(2))` simplifies to `-4 sqrt(2)`?

So -2 + 2(sqrt(2)) simplifies to -4 sqrt(2)? This doesn't seem right

We are arbitrarily choosing to multiply here because we want to remove all of the root 4s because the question wants the answer in the format 4 + root2 /14, do you want me to give u like a 5 min tutoring session to explain this its kinda hard over text

Tht is not allowed - you are not to offer tutoring.

We are arbitrarily choosing to multiply here because we want to remove all of the root 4s because the question wants the answer in the format 4 + root2 /14, do you want me to give u like a 5 min tutoring session to explain this its kinda hard over text

Nah it kind of makes sense now that I know what's happening and when I should be doing it, plus I have too much ground to cover before the next exam and should move on from surds already, and hope to god they don't come up on the next exam 😂 Thanks for your help I appreciate it

Can anyone explain this one? Specifically why/how -2 sqrt(4) sqrt(2) on the third becomes -4 sqrt(2) on the fourth line? I get that the sqrt(4) becomes 2 but apart from that it makes no sense to me. If we're multiplying the -2 coefficient by 2 and sqrt(2), why do we do this randomly here when nothing else is being multiplied and we've already multiplied out the brackets earlier?

We have the term 2 root 8 but we want to show everything as root two.
So we break 8 into 4 x 2 and so it becomes 2 (root 4 x root 2) and we know root 4 is 2
Does that help?