Question

Please help me with 6-14.

Answer 1

5) 7√5


6) 6√3 - 2√27, or 2√27 = 2√(3² x 3)= 2x3√3 = 6√3, hence 6√3 - 6√3 =0

7) √5 . √20 = √(5.20) =√100 = 10

8) -3/√2. multiply numerator & denominator by √2 ==>(-3√2)/(√2 .√2) =-3√2/2

9) √5 (6√2 - √5)  = 6√10 - 5

10) (4-√3)(2+√3) = 8+√3 - 2√3-3 = 5-√3

11) (5+√3)². It's of the form of (a+b)² = a²+2ab+b² ==> 28+10√3

12) (9-√5)(9+√5) .It's of the form of (a-b)(a+b) =a² -b² =49-5 = 44

13) The conjugate of (a+√b) is (a-√b). Multiply numerator & denominator by the conjugate: 6(8+√2)/(8-√2)(8+√2) = (48+6√2)/(64-4) =48+6√2)/60
Simplify by 6 ===> (8+√2)/10

14) (2+√2) /(1-√2). Multiply by the conjugate of the denominator:
       (2+√2)(1+√2)/(1-√2)(1+√2) = . (4+3√2) / 1-2 = - (4+3√2)= -4-3√2