How do you simplify Surds?

Would anyone like to help me with this question?

simplify fully (√x + √9y)(√x - 3√y)

Thank you for your time.

The first step would be to use FOIL to expand the brackets as you would normally. Could you please post your workings so that we can see which bit in particular you need help on?

(edited 6 years ago)

Reply 2

Zain_Ahmed

Original post by K-Man_PhysCheM

The first step would be to use FOIL to expand the brackets as you would normally. Could you please post your workings so that we can see which bit in particular you need help on?

I need help on simplifying the surds.

Reply 3

0zzu

Original post by Zain_Ahmed

I need help on simplifying the surds.

Well, you have to expand the brackets first. If you can't do that, then there's no use in knowing how to simplify surds. Also:

sqrt(3) * sqrt(5) = sqrt(3 * 5)

if that helps.

Reply 4

K-Man_PhysCheM

Original post by Zain_Ahmed

I need help on simplifying the surds.

It's quite a strange question because the surds don't simplify particularly nicely. EDIT: I misinterpreted question because of missing brackets in OP; it actually simplifies very nicely and is a difference of two squares.

Nevertheless:

\sqrt{x} \times \sqrt{x}

is the same as

(\sqrt{x})^2

, which simplifies to...?

\sqrt{9}

is what positive integer...?

and

y\sqrt{y} \equiv \sqrt{y^2} \times \sqrt{y} \equiv \sqrt{y^2 \times y}

, which simplifies to...?

Can you post your working to check?

(edited 6 years ago)

Reply 5

ᒍack

Is it something like X - 9Y?

Reply 6

Zain_Ahmed

Original post by K-Man_PhysCheM

It's quite a strange question because the surds don't simplify particularly nicely.

Nevertheless:

\sqrt{x} \times \sqrt{x}

is the same as

(\sqrt{x})^2

, which simplifies to...?

\sqrt{9}

is what positive integer...?

and

y\sqrt{y} \equiv \sqrt{y^2} \times \sqrt{y} \equiv \sqrt{y^2 \times y}

, which simplifies to...?

Can you post your working to check?

I can't work it out, i can simplify brackets without surds, but with surds is a whole new thing... :frown:

Reply 7

Zain_Ahmed

Original post by ᒍack

Is it something like X - 9Y?

#

can you show me how you got that, i don't have the answers, but could you explain please.

Reply 8

K-Man_PhysCheM

Original post by Zain_Ahmed

I can't work it out, i can simplify brackets without surds, but with surds is a whole new thing... :frown:

Ok, can you at least write out what you've got so far?

eg

(\sqrt{x}+\sqrt{(9y)})(\sqrt{x}-3\sqrt{y}) \equiv \sqrt{x}(\sqrt{x} -3\sqrt{y}) + 3\sqrt{y}(\sqrt{x}-3\sqrt{y})

That's the first bit of expansion. Where would you go from there? Post your working!

(edited 6 years ago)

Reply 9

ᒍack

I'm not 100% if it's correct, see if Mr K_man can help ya.

With thing like this you need to know the laws of surds and their rules fairly well.

Reply 10

K-Man_PhysCheM

Original post by ᒍack

I'm not 100% if it's correct, see if Mr K_man can help ya.

With thing like this you need to know the laws of surds and their rules fairly well.

Your answer is correct, it's just that on this forum we prefer to help students along rather than straight up give an answer, so that they may think about the question, work through the problem themselves and that way learn better. We'd usually only give a worked solution if the student is really struggling even after a while of coaxing. Nevertheless, thanks for the contribution, just don't go straight to the solution next time :smile:

Reply 11

ᒍack

Original post by K-Man_PhysCheM

Yeah honestly I wasn't even too sure myself, I'm not the greatest with surds, and sure thing. When I start in September I reckon i'm going to be posting a lot, it's a good way so you can identify where they're going wrong so they don't do it in the exam :biggrin: