Question

(2+root2)×(3-root5)÷(3+root5)×(2-root2)

Answer 1

Answer:

Step-by-step explanation:

2√3 - √5/ 2√2 + 3 √3

= 2√3-{√5/2√2*-2√2/-2√2} +3√3

=2√3-{ -2√10/-4*2} +3√3

= 2√3-{√10/4} +3√3

= 2√3 - √10/4 + 3√3

=8√3 - √10 + 12√3/4

= 20√3 -√10/4

Answer 2

Answer:

(2+√2)×(3-√5)÷(3+√5)×(2- √2)

multiply the conjugate

={ (2+√2)²×(3-√5)² }÷ { (3²-√5²)×(2²- √2²)}

= { ( 4 + 4√2 + 2 ) ( 9 - 6 √5 + 5 ) } ÷ { ( 9 - 5 ) ( 4 - 2 ) }

=  { (6 + 4√2 )( 14 - 6√5 ) } ÷ { 4 * 2 }

= ( 3 + 2√2 ) ( 7 - 3 √5 ) ÷ 2

= (21 - 9√5 + 14 √2 - 6 √10 ) ÷2

= 0.85 ( answer )

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