Surds help

Original post by SBizzy

Could someone help me with this question, I know the answer and you get the answer. But I don't understand how to get the answer properly.
Question; (3+15)2(Squared)

Give your answer in the form n+m/5 where n and m are integers. Toal 4 marks.

Can you put a picture of the original question please?

Reply 2

Shaanv

17

Can u post a picture of the question or clarify how u have written the question?

Reply 3

OP

Screen Shot 2017-10-23 at 4.39.49 pm.png

Original post by atsruser

Can you put a picture of the original question please?

Reply 4

OP

Original post by Shaanv

Can u post a picture of the question or clarify how u have written the question?

Reply 5

Moriheru

Expand using the binomial theorem. You will be left with two numbers 3 and 15 their sum will be n. For m you are left with 2sqrt(15*3), which is sqrt(45) which is equal to sqrt(3^2*5).The root of 3^2 is 3. You are done.
P.S. 45=15*3 in case you were wondering where the 45 came from.

(edited 6 years ago)

Reply 6

RogerOxon

21

Original post by SBizzy

Could someone help me with this question, I know the answer and you get the answer. But I don't understand how to get the answer properly.
Question; (3+15)2(Squared)

Give your answer in the form n+m/5 where n and m are integers. Toal 4 marks.

What have you tried?

Hint:

\sqrt{15}=\sqrt{3}\sqrt{5}

\therefore (\sqrt{3}+\sqrt{15})^2=3(1+\sqrt{5})^2

Reply 7

AmmarTa

18

Original post by Moriheru

Expand using the binomial theorem. You will be left with two numbers 9 and 15 their sum will be n. For m you are left with 2sqrt(15*3), which is sqrt(45) which is equal to sqrt(3^2*5).The root of 3^2 is 3. You are done.
P.S. 45=15*3 in case you were wondering where the 45 came from.

Binomial theorum is unnecessary for this level of question.

Reply 8

Moriheru

Original post by AmmarTa

Binomial theorum is unnecessary for this level of question.

That is simply what is called multiplying out brackets(at least in this case).... I just multiplied brackets out, which I believe is also using the binomial theorem technically :biggrin:

even though you don't calculate coefficients with factorials etc.

(edited 6 years ago)

Reply 9

AmmarTa

18

Original post by Moriheru

That is simply what is called multiplying out brackets(at least in this case).... I just multiplied brackets out, which I believe is also using the binomial theorem technically :biggrin:

even though you don't calculate coefficients with factorials etc.

Technically but this is a GCSE level question (I assume) so I wouldn't try to over complicate the maths and make it harder for the OP to understand :P

Reply 10

Moriheru

Original post by AmmarTa

Technically but this is a GCSE level question (I assume) so I wouldn't try to over complicate the maths and make it harder for the OP to understand :P

Yes ofc

I just seriously thought that using the binomial theorem is what you called the simple procedure...

Reply 11

OP

Original post by Kambu

This is how i expect they want you to do it. Multiply out the brackets and realise that root 45 can be broken down into two seperate roots... one of which is root 9...which is just 3. So it all works out nicely :smile:

Thank you very much!!!!!!!!!!

OP

Original post by Moriheru

Expand using the binomial theorem. You will be left with two numbers 3 and 15 their sum will be n. For m you are left with 2sqrt(15*3), which is sqrt(45) which is equal to sqrt(3^2*5).The root of 3^2 is 3. You are done.
P.S. 45=15*3 in case you were wondering where the 45 came from.

Binomial isn't needed for this question. You would be overcomplicating the problem too much.

Original post by Kambu

This is how i expect they want you to do it. Multiply out the brackets and realise that root 45 can be broken down into two seperate roots... one of which is root 9...which is just 3. So it all works out nicely :smile:

You aren't meant to post the entire answers. Please read the rules. You are meant to guide them step by step.

Reply 14

NotNotBatman

20

Original post by SBizzy

Could someone help me with this question, I know the answer and you get the answer. But I don't understand how to get the answer properly.
Question; (3+15)2(Squared)

Give your answer in the form n+m/5 where n and m are integers. Toal 4 marks.

(a+b)^2 = (a+b)(a+b) = a^2+2ab+b^2

by distributing.

This is something you should remember; squaring a bracket with two terms results in the the first term squared + 2 times the product of the terms + the other term squared.

Reply 15

y.u.mad.bro?

21

Original post by SBizzy

What would you do to rationalise this?

Take this example. If I have

Unparseable latex formula:

\frac 2\sqrt 2

I would multiply it by

\frac{\sqrt2}{\sqrt{2}}

to get

\frac{2\sqrt2}{2}

which simplifies to

\sqrt 2

Reply 16

Loci Pi

16

Original post by SBizzy

You would use difference of two squares for the numerator:

(a+b)(a-b) = a^2 - b^2

You can substitute the numbers into a and b and simplify like I have done above.

Then you can rationalise the denominator by multiplying both the numerator and denominator by the square root of 31, and simplifying the fraction if possible. :smile:

Reply 17

OP