8-((4^((9)/(4))sqrt(2*2^(2)))/(2sqrt(2^(-2))))^(1/2)

[ 8- ((4^(9/4 ) sqrt(2.2 ^2))/( 2 sqrt( 2^(-2))))^(1/2) ] is equal to

((2-sqrt(2))(2+sqrt(2)))/(4-2sqrt(2))

sqrt(2)x^(2)+9x+4sqrt(2)

3sqrt(2^(5))sqrt(4^(9))sqrt(8)=

Prove the following identities. ((a+2)^(2)(a-3)+(a^(2)-4)sqrt(a^(2)-9))/((a-2)^(2)(a+3)+(a^(2)-4)sqrt((a^(2)-9)))=((a+2)sqrt(a-3))/((a-2)sqrt((a+3))) (a ge 3) .

Integrate (8)/(sqrt(1-(4x)^(2)))+(27)/(sqrt(1-9x^(2)))-(15)/(1+25x^(2)) with respect to x .

Lt_(x to oo) (sqrt(3+9x^(2))+sqrt(4x^(2)-1))/(sqrt(1+16x^(2))-sqrt(9x^(2)+2))=

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

The shortest distance between line y-x=1 and curve is : (1)(sqrt(3))/(4) (2) (3sqrt(2))/(8) (3) (8)/(3sqrt(2))(4)(4)/(sqrt(3))