Respuestas
a) (2/3)^2÷(8/15)+√(25/81)×(1/10)
= (2^2/3^2)÷(8/15)+[(√25)/(√81)]×(1/10)
=(4/9)÷(8/15)+(5/9)×(1/10)
=(4×15)/(9×8)+(5×1)/(9×10)
=60/72+5/90
=5/6+1/18=(5×3+1)/18=16/18=8/9
= 8/9
b) 3√(1/2-3/8)+(1-2/5)÷0,1
= 3√((4×1-3)/8)+(5×1-2)/5÷(1/10)
= 3√(1/8)+(3/5)÷(1/10)
= (1/2) + (3×10)/(5×1)
= (1/2) + 30/5
= 1/2 + 6= (1+2×6)/2=13/2
=13/2 = 6,5
c) 3√0,125=3√(125/1000)=3√125/3√1000
= 5/10=1/2=0,5
d) (3/2)^3÷(15/4)-(8/5)×(1-3/4)
= (3^3/2^3)÷(15/4)-(8/5)×(1/4)
=(27/8)÷(15/4)-(8×1)/(5×4)
=(27×4)/(8×15)-8/20
=9/10-4/10=(9-4)/10=5/10=1/2=0,5
e) √1,44×√0,01+(0,23×10-1,7)^2
= √(144/100)×√(1/100)+(2,3-1,7)^2
= (√144/√100)×(√1/√100)+(0,5)^2
= (12/10)×(1/10)+(1/2)^2=12+1/4
=12/100+0,25=0,12+0,25=0,37
f) 2,5÷5×0,2+√(0,08×2+0,2)×(1,3)^2
=(5/2)÷(5/1)×(2/10)+√(0,16+0,2)×1,69
=(5×1×2)/(2×5×10)+√0,36×1,69
= 10/100+0,6×1,69
= 1/10+1,014=0,1+1,014=1,114
a) (1/3)^2+(1/3)^3. <. 1
= 1/9+1/27
= 3/27+1/27
= 4/27. <. 27/27
b) 0,2^2+0,5×3. >. 2×0,001
= 0,04+1,5. 0,002
= 1,54. >. 0,002
c) 0,3^3×0,1^2+√(1/100). < (4,35-3,2)^2
= 0,027×0,01+√1/√100. <. (1,05)^2
= 0,00027+1/10. < 1,1025
= 0,00027+0,1. < 1,1025
= 0,10027. <. 1,1025
d) (5/4)^2+√(49/16) >. 0,2^3÷0,2^2
=(1,25)^2+7/4. >. 0,2^(3-2)
= 1,5625+1,75. >. 0,2^1
= 3,3125. >. 0,2
e) 0,55+0,24×4. > 3√(27/8)-5/6
=0,55+0,96. > 3/2-5/6
= 1,51. >. 9/6-5/6=4/6=2/3=0,667
= 1,51. >. 0,67
f)
√(2-1/25)÷0,5 > (1,3^2-0,4^3)×0,1
=√(49/25)÷(1/2) >. (1,69-0,064)×(1/10)
=(7/5)÷(1/2). >. 1,626×(1/10)
=14/5. > 0,1626
= 2,8. >. 0,1626