Radical Expressions

Question

Can some explain to me how to simplify this radical expression √2+√7/√8+√7

Answer 1

I'm guessing you mean (√2+√7)/(√8+√7).

 

If that's true, then the way to solve these is to multiply the numerator and denominator by the CONJUGATE of the denominator.  That is, the denominator is √8+√7, so the conjugate is √8-√7.  Then you can use the rule about the difference between two squares to get rid of the radicals in the denominator.

 

√2+√7       √8-√7

---------  x ----------- =

√8+√7       √8-√7

 

(√2+√7) (√8-√7)

-----------------------  =

 (√8+√7) (√8-√7)

 

(√2+√7) (√8-√7)

-----------------------  =

(√8)² - (√7)²

 

√16 - √14 + √56 - √49

------------------------------  =

        8 - 7

 

4 - √14 + √56 -7

----------------------  =

          1

 

-3 + √56 - √14 =

-3 + √14 (√4 - 1) =

-3 + √14 (2 - 1) =

-3 + √14 (1) =

-3 + √14