Odpowiedź:
zad1
[tex](\frac{1}{2} +\frac{1}{4} )^2=(\frac{2}{4} +\frac{1}{4} )^2=(\frac{3}{4} )^2=\frac{9}{16}[/tex]
[tex](\frac{1}{2} )^2+(\frac{1}{4} )^2=\frac{1}{4} +\frac{1}{16} =\frac{4}{16} +\frac{1}{16} =\frac{5}{16}[/tex]
[tex](\frac{1}{2} +\frac{1}{4} )^2>(\frac{1}{2})^2 +(\frac{1}{4})^2[/tex]
zad2
3⁰+(3⁴)²:(3²)³-3=1+3⁸:3⁶-9=-8+3⁸⁻⁶=-8+3²=-8+9=1
zad3
a)6⁹:6⁷=6⁹⁻⁷=6²=36
b)3⁴*3²=3⁴⁺²=3⁶=729
c)[tex]((\frac{1}{2})^2)^3=(\frac{1}{2} )^6 =\frac{1}{64}[/tex]
zad4
a)4³=(2²)³=2⁶
b)2⁷*8²=2⁷*(2³)²=2⁷*2⁶=2⁷⁺⁶=2¹³
c)2⁹:16=2⁹:2⁹⁻⁴=2⁵
zad5
a)34 000 000=3,4*10⁷
b)0,000 00876=8,76*10⁻⁶
zad6
[tex](\frac{2^{30}:2^{14}}{2^8*2^3})^3 *(2^3)^4=(\frac{2^{16}}{2^{11}} )^3:2^{12}}=(2^5)^3:2^{12}}=2^{15}}:2^{12}}=2^3=8[/tex]
zad7
a)(√5)²-(√2)²=5-2=3
b)9*(√7)²-7√3²=9*7-7*3=63-21=42
zad8
a)√81+√121 +√100=9+11+10=30
b)[tex]\sqrt[3]{27} -\sqrt[3]{-64} =3-(-4)=3+4=7[/tex]
zad9
wzór na obwód prostokoąta:
a)L=2a+2b
a=4√7 cm
L=12√7 cm
12√7=2*4√7+2b
12√7-8√7=2b
4√7=2b /:2
b=2√7 cm
odp. drugi bok tego prostokąta =2√7 cm
b)wzór na pole prostokąta:
P=a*b
P=4√7*2√7=8√7²
P=8*7=56 cm²
Odp.Pole tego prostokąta =56 cm²
zad10
√6
[tex]\sqrt{\frac{64}{9} } =\frac{8}{3} =2\frac{2}{3}[/tex]
0,8=4/5
[tex]\sqrt{7\frac{1}{2} } =2,74[/tex]
2
4/5 ;2;√6;[tex]\sqrt{\frac{64}{9} }[/tex];[tex]\sqrt{7\frac{1}{2} }[/tex]
Szczegółowe wyjaśnienie:
