a) 2/√2 + 1
b) 4/√7 - √3
c) √2/√2 - 1
d) (√5-√2)/√5 + √2
e) √10/√10-√5
a) 2/√2 + 1*(√2 - 1)/(√2 - 1)= 2(V2-1)
b) 4/(√7 - √3)*(√7 + √3)/(√7 + √3)=4(√7 + √3)/4=(√7 + √3)
c) √2/(√2 - 1)*(√2 + 1)/(√2 + 1)=V2(√2 + 1)=2+V2
d) (√5-√2)/(√5 + √2)*(√5 - √2)/(√5 - √2)=(√5 - √2)²=5-2V2+2=7-2V2
e) √10/(√10-√5)*(√10+√5)/(√10+√5)=V10 (√10+√5)/5=(10+V50)/5=(10+25V5)/5=2+5V5
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Verified answer
a) 2/√2 + 1*(√2 - 1)/(√2 - 1)= 2(V2-1)
b) 4/(√7 - √3)*(√7 + √3)/(√7 + √3)=4(√7 + √3)/4=(√7 + √3)
c) √2/(√2 - 1)*(√2 + 1)/(√2 + 1)=V2(√2 + 1)=2+V2
d) (√5-√2)/(√5 + √2)*(√5 - √2)/(√5 - √2)=(√5 - √2)²=5-2V2+2=7-2V2
e) √10/(√10-√5)*(√10+√5)/(√10+√5)=V10 (√10+√5)/5=(10+V50)/5=(10+25V5)/5=2+5V5