Question

Help!

1. На сколько sqrt(9+sqrt(65))*sqrt(9-sqrt(65) меньше 14?
2.Вычислите sqrt(3sqrt3(18))*sqrt6(96)

Answer 1

1)
$sqrt{9 + sqrt{65} } times sqrt{9 - sqrt{65} } = sqrt{(9 + sqrt{65} )(9 - sqrt{65}) } = sqrt{{9}^{2} - {( sqrt{65} )}^{2} } = sqrt{81 - 65} = sqrt{16} = 4 \ 14 - 4 = 10$
Ответ: на 10.

2)
$sqrt{3 sqrt[3]{18} } times sqrt[6]{96} = sqrt{ sqrt[3]{27 times 18} } times sqrt[6]{96} = sqrt[6]{27 times 18} times sqrt[6]{96} = sqrt[6]{27 times 18 times 96} = sqrt[6]{ {3}^{3} times 2 times {3}^{2} times 3 times 32 } = sqrt[6]{ {3}^{6} times 64} = sqrt[6]{ {3}^{6} } times sqrt[6]{64} = 3 times 2 = 6$
Ответ: 6