Question

Calculati : a) Radical din 5x+1 , unde x = 1 +6 +6^2 +6^3 + ... + 6^2015
b) Radical din (-2)^8 x (-3)^4 x 5^2 - radical din (-2)^4 x (+3)^2 x (-5)^2
c) (Radical din 432964 - Radical din 101124) : Raducal din 7225

Answer 1

a)  x=1+6 +6^2 +6^3 + ... + 6^2015 =(6^2016-1)/5  (exista aceasta formula)

√(5x+1) = √[5×(6^2016-1)/5+1]=√(6^2016-1+1)=
=√6^2016=√(6^1008)^2=6^1008


b) √(-2)^8 x (-3)^4 x 5^2 - √(-2)^4 x (+3)^2 x (-5)^2=
=√2^8 x 3^4 x 5^2 - √2^4 x 3^2 x 5^2=
=2^4 x 3^2 x 5 - 2^2 x 3 x 5=
=2^2 x 3 x 5 x(2^2x3 -1)=
=2^2 x 3 x 5x 11=
=660

c) (√432964 - √101124) : √7225=(658-318):85=340:85=4