Question

Будь ласка, розв'яжіть, дам 35 балів ​

Answer 1

Ответ:

Объяснение:

1)

$\sqrt{20}=\sqrt{4*5}=\sqrt{2^{2} *5}=2\sqrt{5}$

$\sqrt{500}=\sqrt{5*100} =\sqrt{5*10^{2} } =10\sqrt{5}$

$\sqrt{72x^{12} }=\sqrt{36*2(x^{3} )^{4} } =\sqrt{6^{2}*2 (x^{3} )^{4}} =6x^{2} \sqrt{3x^{3} }$

2)

$2\sqrt{11}=\sqrt{2^{2} *11} =\sqrt{4*11}=\sqrt{44}$

$2\sqrt{8}=\sqrt{2^{2} *8}=\sqrt{4*8}=\sqrt{32}$

$-x^{3} \sqrt{7x^{9} }=-\sqrt{(x^{3} )^{2} *7x^{9}}=-\sqrt{x^{6}*7x^{9} } =-\sqrt{7x^{15} }$

3)

1. $\sqrt{4a}+\sqrt{49a}-\sqrt{121a}=2\sqrt{a} +7\sqrt{a} -11\sqrt{a} =-2\sqrt{a}$

2. $6\sqrt{27a} -8\sqrt{48a}-2\sqrt{75a}= 6\sqrt{3^{2}*3 a}-8\sqrt{4^{2}*3 a}-2\sqrt{5^{2}*3 a}=$

= $6*3\sqrt{3a} -8*4\sqrt{3a} -2*5\sqrt{3a} =18\sqrt{3a} -32\sqrt{3a} -10\sqrt{3a}=$

$=-24\sqrt{3a}$

3. $(12\sqrt{2}-2\sqrt{50} +3\sqrt{98} )\sqrt{2} =(12\sqrt{2}-2\sqrt{5^{2}*2 } +3\sqrt{7^{2}*2} )\sqrt{2} =$

$=(12\sqrt{2}-2*5\sqrt{2} +3*7\sqrt{2} )\sqrt{2}=(12\sqrt{2}-10\sqrt{2} +21\sqrt{2} )\sqrt{2}=$

$=23\sqrt{2} *\sqrt{2}=23*2=46$

4. $(\sqrt{19} -\sqrt{10} )(\sqrt{19} +\sqrt{10} )=\sqrt{19}^{2} -\sqrt{10}^{2} =19-10=9$

4)

$\frac{14}{\sqrt{7} } *\frac{\sqrt{7}}{\sqrt{7}} =\frac{14\sqrt{7}}{7}$

$\frac{3}{\sqrt{6} } *\frac{\sqrt{6}}{\sqrt{6}} =\frac{3\sqrt{6}}{6}$

$\frac{45}{8\sqrt{5} } *\frac{\sqrt{5}}{\sqrt{5}} =\frac{45\sqrt{5}}{8*5} =\frac{45\sqrt{5}}{40}=\frac{9\sqrt{5}}{8}$