Surds Question (GCSE)

?18 + 10
-------------
?2

Write the answer in the form p + q?2, where p and q are integers

I can't seem to get my head round it.

Any help would be appreciated :smile:

:smile:

edit: the '?' are supposed to be square route signs, not sure what happened...

MostCompetitive

Original post by Kieran?

I can't seem to get my head round it.

Any help would be appreciated :smile:

:smile:

edit: the '?' are supposed to be square route signs, not sure what happened...

\frac{\sqrt 18 + 10}{\sqrt 2}

\sqrt 18 = \sqrt 9\sqrt 2 = 3\sqrt 2

so it's simply

\frac{3\sqrt 2}{\sqrt2} + \frac{10}{\sqrt 2}

Spoiler

(edited 12 years ago)

From above ,

Then rationalise the denominator of each fraction by multiplying both top and bottom by root 2 and you should get the answer in that form.

OP

Original post by MostCompetitive

\frac{\sqrt 18 + 10}{\sqrt 2}

\sqrt 18 = \sqrt 9\sqrt 2 = 3\sqrt 2

so it's simply

\frac{3\sqrt 2}{\sqrt2} + \frac{10}{\sqrt 2}

Then you would rationalise them to give 6 + 10 ?2 (cant do your fancy code)

I was trying to rationalise it first. Makes sense now, thanks

MostCompetitive

Original post by Kieran?

Then you would rationalise them to give 6 + 10 ?2 (cant do your fancy code)

I was trying to rationalise it first. Makes sense now, thanks

Are you sure? Have another look and/or see the spoiler in my original post

You're welcome btw :smile:

:smile:

OP

Original post by MostCompetitive

Are you sure? Have another look and/or see the spoiler in my original post

You're welcome btw :smile:

:smile:

How does 10/?2 = ?50

And how does 3?2/?2 become 3 :confused:

:confused:

MostCompetitive

Original post by Kieran?

How does 10/?2 = ?50

And how does 3?2/?2 become 3 :confused:

:confused:

1)

\frac{3\sqrt 2}{\sqrt 2} = 3

because

\frac{3\sqrt 2}{\sqrt 2} = 3

x

\frac{\sqrt 2}{\sqrt 2}

. How many times does root 2 go into root 2?

2)

\frac{10}{\sqrt 2} = \sqrt 50

because, if you square the fraction, you get

\frac{100}{2}

but, of course, you have to square root that now because you've squared it.

\frac{100}{2} = 50

so it is simply

\sqrt 50

.

Ask if you're still unsure :smile:

:smile:

(edited 12 years ago)

OP

Original post by MostCompetitive

1)

\frac{3\sqrt 2}{\sqrt 2} = 3

because

\frac{3\sqrt 2}{\sqrt 2} = 3

x

\frac{\sqrt 2}{\sqrt 2}

. How many times does root 2 go into root 2?

2)

\frac{10}{\sqrt 2} = \sqrt 50

because, if you square the fraction, you get

\frac{100}{2}

but, of course, you have to square root that now because you've squared it.

\frac{100}{2} = 50

so it is simply

\sqrt 50

.

Ask if you're still unsure :smile:

:smile:

I've just realised what I've done wrong. I did it a different way to you but when I thought that the answer was 6 + 10 ?2 it was actually 6+ 10 ?2 / 2

So that would equal 3 + 5 ?2 which is the right answer :tongue:

:tongue:

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