Question

Номера 17, 18, 19, 20
Заранее спасибо ​

Answer 1

17.

1) $\sqrt{12+6\sqrt{3} } =\sqrt{(3+\sqrt{3})^{2}  } =3+\sqrt{3}$

2) $\sqrt{6+4\sqrt{2}  } =\sqrt{(2+\sqrt{2})^{2}  } =2+\sqrt{2}$

3) $\sqrt{27-10\sqrt{2} } =\sqrt{(5-\sqrt{2}) ^{2} } =5-\sqrt{2}$

4) $\sqrt{14-6\sqrt{5} } =\sqrt{(3-\sqrt{5}) ^{2}} =3-\sqrt{5}$

18.

1) $\sqrt{\sqrt{n^{4} } } =\sqrt{n^{2} } =n$

2) $\sqrt{\sqrt{n^{8} } } =\sqrt{n^{4} } =n^{2}$

3) $\sqrt{\sqrt{\sqrt{a^{16} } } } =\sqrt{\sqrt{a^{8} } } =\sqrt{a^{4} } =a^{2}$

4) $\sqrt{\sqrt{\sqrt{a^{24} } } } =\sqrt{\sqrt{a^{12} } } =\sqrt{a^{6} } =a^{3}$

5) $\sqrt{\sqrt{m^{4} } } =\sqrt{m^{2} } =m$

6) $\sqrt{\sqrt{m^{12} } } =\sqrt{m^{6} } =m^{3}$

19.

1) $\sqrt{\sqrt{(x-1)^{4} } } =\sqrt{(x-1)^{2} } =x-1$

2) $\sqrt{\sqrt{(x+2)^{4} } } =\sqrt{(x+2)^{2} } =x+2$

3) $\sqrt{\sqrt{(x+2)^{4} } } =\sqrt{(x+2)^{2} } =x+2$

4) $\sqrt{\sqrt{(x-1)^{4} } } =\sqrt{(x-1)^{2} } =x-1$

20.

1) $\sqrt{(\sqrt{97}+4)\sqrt{113-8\sqrt{97} }  } =\sqrt{(\sqrt{97}+4)\sqrt{(4-\sqrt{97})^{2}  }  } =\sqrt{(\sqrt{97}+4)*(\sqrt{97} -4) } =\sqrt{97-16} =\sqrt{81} =9$

2) $\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5} } } }=\sqrt{\sqrt{\sqrt{5}-\sqrt{3-(2\sqrt{5  })^{2}}}}=\sqrt{\sqrt{5} -\sqrt{3-(2\sqrt{5}-3) } } =\sqrt{\sqrt{5} -\sqrt{3-2\sqrt{5}+3 } } =\sqrt{\sqrt{5} -\sqrt{6-2\sqrt{5} } } =\sqrt{\sqrt{5}-\sqrt{(1-\sqrt{5}) ^{2} }  } =\sqrt{\sqrt{5}-(\sqrt{5} -1) } =\sqrt{\sqrt{5}-\sqrt{5}+1  } =\sqrt{1} =1$