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2014-11-04T14:53:45+02:00
7.a)9 \sqrt{3
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b) \sqrt{363} = \sqrt{ 11^{2} *3} =11 \sqrt{3}

c) \sqrt{507}= \sqrt{3* 13^{2} }  =13 \sqrt{3}

d)  \sqrt{1352}= \sqrt{ 2^{3}* 13 ^{2} }  =2*13 \sqrt{2} =26\sqrt{2}

e) \sqrt{47,32}= \sqrt{ \frac{4732}{100} }  =\sqrt{ \frac{ 2^{2} *1183}{100} } = \frac{2}{10} \sqrt{1183}  =0,2 \sqrt{1183}

f) \sqrt{14,45} = \sqrt{ \frac{1445}{100} } = \sqrt{ \frac{5*17 ^{2} }{100} } = \frac{17}{10} \sqrt{5}=1,7 \sqrt{5}

g) \sqrt{5 x^{2} } =x \sqrt{5} ,x Q_{+}

h) \sqrt{3x y^{2} } =y \sqrt{3x} ,x Q_{+} si y Q_{+}

8.a)  2 \sqrt{2} sau  \sqrt{18} ?
 \sqrt{18} = \sqrt{2*3 ^{2} } =3 \sqrt{2}
2 \sqrt{2} < 3 \sqrt{2}

b)5 \sqrt{243} sau 27 \sqrt{27} ?
5 \sqrt{243} =5* \sqrt{3 ^{5} } =5*9 \sqrt{3} =45 \sqrt{3}
27 \sqrt{27}=27 \sqrt{ 3^{3} } =27*3 \sqrt{3} =81\sqrt{3}
5 \sqrt{243} < 27 \sqrt{27}

c)  \sqrt{75} sau 2 \sqrt{50} ?
\sqrt{75}= \sqrt{3*5 ^{2} } =5 \sqrt{3}
2 \sqrt{50}=2* \sqrt{2*5^{2} } =2*5 \sqrt{2}=10 \sqrt{2}
 \sqrt{75} <2 \sqrt{50}