Question

smplify 2 /root of 5+root of 3+1/rootof 3+ root of 2 - 3/root of 5+ root of 2​

Answer 1

Answer:

1) ( 10 - 6√5 ) / 10

2) ( 20√3 - 3√5 + 30√2 ) / 15

Step-by-step explanation:

1) 1/2 + √3 + 2/√5 - √3 + 1/2 - √5

= 1/2 + 2/√5 + 1/2 - √5

= 1/2 + 1/2 - √5 + ( 2/√5 × √5/√5 )

= 1/2 + 1/2 - √5 + 2√5/5

= 5/10 + 5/10 - 10√5/10 + 4√5/10

= 10/10 - 6√5/10

= ( 10 - 6√5 ) / 10

2) 2/√5 + √3 + 1/√3 + √2 - 3/√5 + √2

= -1/√5 + √3 + 1/√3 + 2√2

= ( -1/√5 × √5/√5 ) + √3 + ( 1/√3 × √3/√3 ) + 2√2

= -√5/5 + √3 + √3/3 + 2√2

= -3√5/15 + 15√3/15 + 5√3/15 + 30√2/15

= -3√5/15 + 20√3/15 + 30√2/15

= ( 20√3 - 3√5 + 30√2 ) / 15