Question

How do I solve √ 7/ 3-√ 7 ?
I know the answer is 7+3√ 7/2 but I dont know how I should solve.

Answer 1

Answer:

Whenever there's a a-√b form of number in the denominator always multiply and divide by a+√b

So, that the denominator becomes

(a+√b)(a-√b) = a^2-b

So,

here,

√7/3-√7 , multiplying and dividing by 3+√7

√7(3+√7)/(3+√7)(3-√7) = (3√7+7)/(3^2-7) = 7+3√7/2

Hope this helps you !

I hope you don't have any doubt in the steps ｡◕‿◕｡

Similarly, if you get a+√b type number in denominator, multiply and divide by a-√b

Further in a more complicated case if you ever get a number like

√p+√q type number in denominator

then, divide and multiply by √p-√q, so that the denominator becomes p-q