a=root 8 + 2.

Question

b=root 8 - 2
t=a*2 - b *2.
work out the value of t.give your answer in the form c root 2 where c is an integer.

Answer 1

√8 = √ ( 4 • 2 ) = √4 • √ 2 = 2 √2

a = √8 + 2 = 2√2 + 2

b = √8 - 2 = 2√2 - 2

a^2 - b^2 = ( a + b ) ( a - b ) =

( 2 √2 + 2 + 2 √2 - 2 ) • [ 2 √2 + 2 - ( 2 √2 - 2 ) ] =

+
( 2√2 + 2 √2 ) • ( 2 √2 + 2 - 2 √2 + 2 ) =

4√2 • 4 = 16 √2

Answer 2

( 2 √2 + 2 + 2 √2 - 2 ) • [ 2 √2 + 2 - ( 2 √2 - 2 ) ] =

( 2√2 + 2 √2 ) • ( 2 √2 + 2 - 2 √2 + 2 ) =

4√2 • 4 = 16 √2