Question

Buna! Ma puteti ajuta si pe mine la ex 8 . Am mare nevoie de el.Dau coroana.Multumesc anticipat

Answer 1

$\displaystyle\mathtt{a)~-2\sqrt{7}+(-5,2)+3,3+2\sqrt{7}-8=-5,2+3,3-8=}\\\\ \mathtt{=-\frac{52}{10}+\frac{33}{10}+8=\frac{-52+33-80}{10}=-\frac{99}{10} }$

$\displaystyle \mathtt{b)~0,45\cdot\sqrt{27}+1,(3)\cdot\sqrt{3}-\frac{3}{4}\cdot \sqrt{243}=}\\\\\mathtt{=\frac{45}{100}\cdot3\sqrt{3}+\frac{13-1}{9}\cdot \sqrt{3}-\frac{3}{4}\cdot9\sqrt{3}=\frac{135\sqrt{3}}{100}+\frac{12\sqrt{3}}{9}- \frac{27\sqrt{3}}{4}=}\\\\\mathtt{=\frac{1215\sqrt{3}+1200\sqrt{3}-6075\sqrt{3}}{900}=-\frac{3660\sqrt{3}}{900}=-\frac{61\sqrt{3}}{15}}$

$\displaystyle \mathtt{c)~ \Big|\sqrt{75}- \sqrt{125}\Big|+\Big| \sqrt{50}- \sqrt{162}\Big|= \sqrt{125}- \sqrt{75}+ \sqrt{162} - \sqrt{50}=}\\ \\ \mathtt{=5 \sqrt{5}-5 \sqrt{3}+9 \sqrt{2}-5 \sqrt{2} =5 \sqrt{5}-5 \sqrt{3}+4 \sqrt{2}}$

$\displaystyle \mathtt{d)~\Big| \sqrt{12}- \sqrt{63}+ \sqrt{112}- \sqrt{108}\Big|-\Big| \sqrt{28}- \sqrt{175}- \sqrt{300}\Big|= }\\ \\ \mathtt{=\Big|2 \sqrt{3}-3 \sqrt{7}+4 \sqrt{7}-6 \sqrt{3}\Big|-\Big|2 \sqrt{7}-5 \sqrt{7}-10 \sqrt{3}\Big|=}\\ \\ \mathtt{=\Big|-4 \sqrt{3}+ \sqrt{7}\Big|-\Big|-3 \sqrt{7}-10 \sqrt{3}\Big|=4 \sqrt{3}- \sqrt{7} -\left(3 \sqrt{7}+10 \sqrt{3}\right)= }\\ \\ \mathtt{=4 \sqrt{3}- \sqrt{7}-3 \sqrt{7}-10 \sqrt{3}=-6 \sqrt{3}-4 \sqrt{7} }$

$\displaystyle \mathtt{e)~- \sqrt{5}\cdot\left( \sqrt{3}- \sqrt{5}\right)=- \sqrt{5}\cdot \sqrt{3}- \sqrt{5} \cdot \left(-\sqrt{5}\right)=- \sqrt{15}+5}$

$\displaystyle \mathtt{f)~-2\cdot\left( \sqrt{2}+ \sqrt{3} - \sqrt{5} \right)=-2 \sqrt{2}-2 \sqrt{3}+2 \sqrt{5}}$

$\displaystyle \mathtt{g)~20-\left(-3 \sqrt{3}-5 \sqrt{5}\right)\cdot \sqrt{3}=20-\left(-3 \sqrt{3}\cdot \sqrt{3} -5 \sqrt{5}\cdot \sqrt{3}\right)=}\\ \\ \mathtt{=20-\left(-9-5 \sqrt{15}\right)=20+9+5 \sqrt{15} =29+5 \sqrt{15} }$

$\displaystyle \mathtt{h)~ \sqrt{125}-\left(2 \sqrt{10}-4 \sqrt{2}\right)\cdot\left(- \sqrt{5}\right)=5 \sqrt{5}-\left(-2 \sqrt{50}+4 \sqrt{10}\right)= }\\ \\ \mathtt{=5 \sqrt{5}-\left(-2\cdot5 \sqrt{2}+4 \sqrt{10}\right)=5 \sqrt{5}-\left(-10 \sqrt{2}+4 \sqrt{10}\right)=}\\ \\ \mathtt{=5 \sqrt{5}+10 \sqrt{2}-4 \sqrt{10}}$

$\displaystyle \mathtt{i)~2 \sqrt{3}\cdot5 \sqrt{2}-3 \sqrt{2}\cdot \sqrt{3}-4 \sqrt{2}\cdot5 \sqrt{3} -6 \sqrt{3} \cdot5 \sqrt{2}-2 \sqrt{3}\cdot \sqrt{2}= }\\ \\ \mathtt{=10 \sqrt{6} -3 \sqrt{6}-20 \sqrt{6}-30 \sqrt{6}-2 \sqrt{6}=-45 \sqrt{6} }$

$\displaystyle \mathtt{j)~ \sqrt{24} : \sqrt{2}-12 \sqrt{60}:2 \sqrt{5} +4\cdot2\cdot \sqrt{3}= }\\ \\ \mathtt{=\sqrt{12}-12\cdot2 \sqrt{15}\cdot \frac{1}{2}\cdot \sqrt{5} +8 \sqrt{3}=2 \sqrt{3} - 12 \sqrt{15}\cdot \sqrt{5} +8 \sqrt{3}= }\\ \\ \mathtt{=2 \sqrt{3}-12 \sqrt{75}+8 \sqrt{3}=2 \sqrt{3}-12\cdot5 \sqrt{3}+8 \sqrt{3} =}\\ \\ \mathtt{=2 \sqrt{3}-60 \sqrt{3} +8 \sqrt{3}=-50 \sqrt{3} }$

$\displaystyle \mathtt{k)~ \sqrt{90}: \sqrt{10}\cdot \sqrt{11}= \sqrt{9}\cdot \sqrt{11}=3 \sqrt{11} }$

$\displaystyle \mathtt{l)~ \sqrt{2}\cdot\left(3 \sqrt{5}- \sqrt{2}\right)- \sqrt{5}\cdot \left(2 \sqrt{2}-4 \sqrt{5}\right)=}\\ \\ \mathtt{= \sqrt{2}\cdot3 \sqrt{5}- \sqrt{2}\cdot \sqrt{2}- \sqrt{5}\cdot2 \sqrt{2}- \sqrt{5}\cdot\left(-4 \sqrt{5}\right) \right)=}\\ \\ \mathtt{=3 \sqrt{10}-2-2 \sqrt{10}+20= \sqrt{10} +18}$