Автор - alexander0309

Номера 17, 18, 19, 20
Заранее спасибо ​

Ответ

Автор - khristolyubovnik00

17.

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

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

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

4) sqrt{14-6sqrt{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{113-8sqrt{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{29-12sqrt{5} } } }=sqrt{sqrt{sqrt{5}-sqrt{3-(2sqrt{5  })^{2}}}}=sqrt{sqrt{5} -sqrt{3-(2sqrt{5}-3) } } =sqrt{sqrt{5} -sqrt{3-2sqrt{5}+3 } } =sqrt{sqrt{5} -sqrt{6-2sqrt{5} } } =sqrt{sqrt{5}-sqrt{(1-sqrt{5}) ^{2} }  } =sqrt{sqrt{5}-(sqrt{5} -1) } =sqrt{sqrt{5}-sqrt{5}+1  } =sqrt{1} =1

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