Решение.
Применяем формулу разности [tex]\boldsymbol{\bf (a-b)(a+b)=a^2-b^2}[/tex] и формулу
[tex]\boldsymbol{\bf \sqrt[n]{x}\cdot \sqrt[n]{y}=\sqrt[n]{xy}}[/tex]
[tex]\boldsymbol{\bf \sqrt[4]{4-\sqrt{15}}\cdot \sqrt[4]{4+\sqrt{15}}}=\boldsymbol{\sqrt[4]{(4-\sqrt{15})(4+\sqrt{15})}}=\boldsymbol{\sqrt[4]{4^2-(\sqrt{15})^2}=}\\\\\\\boldsymbol{=\sqrt[4]{16-15}=\sqrt[4]{1}=1}[/tex]
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Решение.
Применяем формулу разности [tex]\boldsymbol{\bf (a-b)(a+b)=a^2-b^2}[/tex] и формулу
[tex]\boldsymbol{\bf \sqrt[n]{x}\cdot \sqrt[n]{y}=\sqrt[n]{xy}}[/tex]
[tex]\boldsymbol{\bf \sqrt[4]{4-\sqrt{15}}\cdot \sqrt[4]{4+\sqrt{15}}}=\boldsymbol{\sqrt[4]{(4-\sqrt{15})(4+\sqrt{15})}}=\boldsymbol{\sqrt[4]{4^2-(\sqrt{15})^2}=}\\\\\\\boldsymbol{=\sqrt[4]{16-15}=\sqrt[4]{1}=1}[/tex]