Rationalise the deniminator of the surds.?

Question

1) 5√2
------------
√8 - √7
how can i rationalise the denominator of this, as the ones i have been doing so far were simple ones like this one below:-
1
----------
3 - √7
where i can use the rule.
please help
thanks

Answer 1

You need to multiply the original fraction by [(√8 + √7)/(√8 + √7)], because √8 + √7 is the conjugate of the original denominator. The result will be a new denominator equal to 8 - 7 = 1. The numerator won't be quite as neat as some that you've seen before, but the numerator will have been successfully rationalized.

Answer 2

Question 1
5√2 (√8 + √7) / √[ (√8 - √7) (√8 + √7) ]
5√2 (√8 + √7) / (8 - 1)
5√2 (√8 + √7)
5√16 + 5√14
20 + 5√14

Question 2
(3 + √7) / (9 - 7)
(1/2) (3 + √7)

Answer 3

5√2
------------------
√8-√7

5√2(√8+√7)
--------------------------
(√8-√7)(√8+√7)

now,

(√8-√7)(√8+√7)
(a-b) (a+b) = a²-b²
= (√8²-√7²)
= (8-7)
= 1

So, it becomes

5√2(√8+√7)
--------------------------
1


therefore

5√16+5√14
------------------
1



and as for 2nd one

answer is

1(3+√7)
--------------------
2