Question

15 балов за несложное задание
Обчисліть значення виразу.

Answer 1

$1) sqrt[5]{16} cdotp sqrt[5]{2} =sqrt[5]{16 cdotp 2} =sqrt[5]{32} = 2\\2) sqrt[6]{10000} cdotp sqrt[6]{100} = sqrt[6]{10^{4}} cdotp sqrt[6]{10^{2}} = sqrt[6]{10^{4} cdotp 10^{2}} = sqrt[6]{10^{6}} = 10 \\3) sqrt[3]{0,108} cdotp sqrt[3]{2} = sqrt[3]{0,108 cdotp 2} = sqrt[3]{0,216} = 0,6$

$4) sqrt[8]{3^{5} cdotp 5^{2}} cdotp sqrt[8]{3^{3} cdotp 5^{6}} = sqrt[8]{3^{5} cdotp 5^{2} cdotp 3^{3} cdotp 5^{6}} = sqrt[8]{3^{8} cdotp 5^{8}} = 3 cdotp 5 = 15 \\5) dfrac{sqrt[5]{96}}{sqrt[5]{729}} = sqrt[5]{dfrac{96}{729}} = sqrt[5]{dfrac{32}{243}} = dfrac{2}{3}$

$6) dfrac{sqrt[3]{5^{8} cdotp 7^{10}}}{sqrt[3]{5^{2} cdotp 7^{16}}} = sqrt[3]{ dfrac{5^{8} cdotp 7^{10}}{5^{2} cdotp 7^{16}}} = sqrt[3]{dfrac{5^{6}}{7^{6}}} = dfrac{5^{2}}{7^{2}} = dfrac{25}{49} \\7) sqrt[3]{5 - sqrt{17}} cdotp sqrt[3]{5 + sqrt{17}} = sqrt[3]{(5 - sqrt{17})(5 + sqrt{17})} = sqrt[3]{25 - 17} = sqrt[3]{8} = 2$

$8) sqrt[4]{26 + sqrt{51}} cdotp sqrt[4]{26 - sqrt{51}} = sqrt[4]{(26 + sqrt{51})(26 - sqrt{51})} = sqrt[4]{676 - 51} = sqrt[4]{625} = 5$

$9) sqrt[5]{3sqrt{2} - 5sqrt{2}} cdotp sqrt[5]{3sqrt{2} + 5sqrt{2}} = sqrt[5]{(3sqrt{2} - 5sqrt{2})(3sqrt{2} + 5sqrt{2})} = sqrt[5]{(-2sqrt{2}) cdotp 8sqrt{2}} = sqrt[5]{-32} = -2$