Please help me with the following questions on surds.

Question

1) Expand 5 and square root 5 (square root 6 + 8 and square root 5)

 

2) Expand (Square root 3 - 4 and square root 5)(Square root 7 - 8 and square root 2)

 

USING ONLY DOPS FOR 3 AND 4

 

3) Expand (Square root 5 + square root 3)(Square root 5 - Square root 3)

 

4) Expand (3 and square root 11 + square root 7)(3 and square root 11 - square root 7)

 

 

Answer 1

Hi Jack.

I'm not following numbers 1 and 2 but I'll try.

 1) 5√5(√6+8√5)=5√30+5*8*5=5√30+200

 

 2) (√3-4√5)(√7-8√2)=√21-4√35-8√6+32√10

 

 3) (√5+√3)(√5-√3)=5-3=2

 

 4) (3√11+√7)(3√11-√7)=3*3*11-7=99-7=92