Question

Buna.☝️dau coroana si 30 de puncte

Answer 1

Răspuns

Explicație pas cu pas:

√5 / √45= √1/9 =1/3

√7 /√28= √1/4 =1/2

√3 /√12 =√1/4 =1/2

√48 /√72= 4√3 /6√2= 2√3 / 3√2 =2√6 /6 =√6 /3

√39 /√156= √(13·3) / √(13·12) =√1/4 =1/2

√(5³·7³)=5·7·√(5·7)=35√35

√(2^7· 3³·11^5)=2³·3·11²·√(2×3×11)=24·121·√66=2904·√66

√x^4=x²

√(x^5·y²)=x²·y·√x

Answer 2

Rezolvare :
$a) \frac{ \sqrt{5} }{ \sqrt{45} } = \frac{1}{ \sqrt9} = \frac{1}{3} .$
$b) \frac{ \sqrt{7} }{ \sqrt{28} } = \frac{1}{ \sqrt 4} = \frac{1}{2}$
$c) \frac{ \sqrt{3} }{ \sqrt{12} } = \frac{1}{ \sqrt4} = \frac{1}{2}$
$d) \frac{ \sqrt{48} }{ \sqrt{72} } = \frac{ \sqrt{2} }{ \sqrt{3} } = \frac{ \sqrt{2} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{6} }{3}$
$e) \frac{ \sqrt{39} }{ \sqrt{156} } = \frac{1}{ \sqrt4} = \frac{1}{2}$
$f) \sqrt{ {5}^{3} \times 7 {}^{3} } = \sqrt{(5 \times 7) {}^{3} } = \sqrt{35 {}^{3} } = 35 \sqrt{35}$
$g) \sqrt{2 {}^{7} \times {3}^{3} \times {11}^{5} } = \sqrt{128 \times 27 \times {11}^{5} } = \sqrt{3456 \times 11 {}^{5} } = 24 \times {11}^{2} \times \sqrt{6 \times 11} = 24 \times 121 \sqrt{66} = 2904 \sqrt{66}$
$h) \sqrt{x {}^{4} } = x {}^{2}$
$i) \sqrt{ {x}^{5} \times y {}^{2} } = \sqrt{x {}^{4} \times x \times y {}^{2} } = \sqrt{x {}^{4} } \times \sqrt{ {y}^{2} } \times \sqrt{x} = x {}^{2} y \sqrt{x}$