Odpowiedź:
a) √4⁴ = [tex]\sqrt[2]{4^{4} } = 4^{2} =16\\[/tex]
b) √(-7)² = [tex]\sqrt{49} = 7[/tex]
c) √5⁴ x 2² = [tex]\sqrt[2]{5^{4} }[/tex] × 4 = 5² ×4 = 25 × 4 = 100
d) √8 x 162 = [tex]\sqrt{2^{3} }[/tex] × 162 = [tex]\sqrt{2^{2} * 2^{1} }[/tex] × 162 = [tex]\sqrt{4*2[/tex] × 162 = [tex]2\sqrt{2}[/tex] × 162 =324[tex]\sqrt{2}[/tex] ≈ 458.20
e) √3 x 21 = 21[tex]\sqrt{3}[/tex] ≈ 36,37
f) √27000 x 30 = [tex]\sqrt{ 30^{3}[/tex] × 30 = [tex]\sqrt{ 30^{2} *30^{1}[/tex] × 30 = [tex]\sqrt{ 30^{2}[/tex] × [tex]\sqrt{30}[/tex] × 30 = 30[tex]\sqrt{30}[/tex] × 30 = 900[tex]\sqrt{30}[/tex] ≈ 4929,50
g) √22 500 = [tex]\sqrt{ 150^{2}[/tex] = 150
h) √0,0009 = [tex]\sqrt{ \frac{9}{10000}[/tex] = [tex]\frac{3}{100}[/tex] = 0,03
i) √12,25 = = [tex]\sqrt{ \frac{49}{4}[/tex]= [tex]\frac{7}{2}[/tex] = [tex]3\frac{1}{2}[/tex] = 3,5
j) √4,41 = [tex]\sqrt{ \frac{441}{100}[/tex]= [tex]\frac{21}{10}[/tex] = [tex]2\frac{1}{10}[/tex] = 2,1
Odpowiedź:
a) √4⁴ = 4² = 16
b) √(-7)² = 7
c) √5⁴ x 2² = 5² * 4 = 25 ^4 = 100
d) √(8 x 162) = √1296 = 36
e) √(3 x 21) = √63 = √(9*7) = 3√7
f) √(27000 x 30) = √810000 = 900
g) √22 500 = 150
h) √0,0009 = 0,03
i) √12,25 = 3,5
j) √4,41. = 2,1
Szczegółowe wyjaśnienie: