# Thread: 1 + 3 squareroot 5

1. ## 1 + 3 squareroot 5

(1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers.

What are the values of p and q?

2. Originally Posted by Natasha1
(1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers.

What are the values of p and q?
$\displaystyle (1 + 3 \sqrt{5})^2 = p + q\sqrt{5}$.

Expand the left hand side and match it with the bits you have on the right hand side.

3. Originally Posted by Natasha1
(1 + 3squareroot of 5)squared = p + qsquareroot of 5 where p and q are integers.

What are the values of p and q?
Calculate (1 + 3squareroot of 5)squared

4. what is 2 x 3squareroot of 5?

Should it be treated like (a+b)squared?

asquared + bsquared + 2ab

5. Originally Posted by Natasha1
Should it be treated like (a+b)squared?
Indeed.

6. right right... then lets see, is it

1 + 45 + 6squareroot of 10 = p + qsquareroot of 5

7. Originally Posted by Natasha1
right right... then lets see, is it

1 + 45 + 6squareroot of 10 = p + qsquareroot of 5
Yes. And 1 + 45 = 46. Now compare each side.

8. Originally Posted by Natasha1
right right... then lets see, is it

1 + 45 + 6squareroot of 10 = p + qsquareroot of 5

Hi Natasha1,

It is $\displaystyle 46+6\sqrt{5}$

The 2 is multiplied by the coefficient of the radical, not what's inside.

$\displaystyle 2ab=2(1)(3\sqrt{5})=6\sqrt{5}$

9. so p = 46 and q = 6 but the squareroots are both different? We have a 10 and a 5?

10. Oh so it's 46 + 6squareroot of 5 = p + qsquareroot of 5.

Thanks a million gents!!