Question

calcula$E=\sqrt{3}tan30grados-\sqrt{2} sen45grados$

Answer 1

Respuesta:

$\sqrt{3\tan \left(30^{\circ \:}\right)}-\sqrt{2\sin \left(45^{\circ \:}\right)}\\\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \tan \left(30^{\circ \:}\right)=\frac{\sqrt{3}}{3}\\\mathrm{Utilizar\:la\:siguiente\:identidad\:trivial}:\quad \sin \left(45^{\circ \:}\right)=\frac{\sqrt{2}}{2}\\\sqrt{3}\sqrt{\frac{\sqrt{3}}{3}}-\sqrt{2}\sqrt{\frac{\sqrt{2}}{2}}$

$\sqrt{3}\sqrt{\frac{\sqrt{3}}{3}}-\sqrt{2}\sqrt{\frac{\sqrt{2}}{2}}=\\\sqrt{3}\sqrt{\frac{\sqrt{3}}{3}}=\sqrt{3\cdot \frac{\sqrt{3}}{3}}\\3\cdot \frac{\sqrt{3}}{3}\\\frac{\sqrt{3}\cdot \:3}{3}\\\left(3^{\frac{1}{2}}\right)^{\frac{1}{2}}\\3^{\frac{1}{2}\cdot \frac{1}{2}}\\\sqrt[4]{3}$

$\sqrt{2}\sqrt{\frac{\sqrt{2}}{2}}\\\sqrt{2\cdot \frac{\sqrt{2}}{2}}\\2\cdot \frac{\sqrt{2}}{2}\\\frac{\sqrt{2}\cdot \:2}{2}\\\\\sqrt{2}\\\left(2^{\frac{1}{2}}\right)^{\frac{1}{2}}\\\sqrt[4]{2}$

$\sqrt[4]{3}-\sqrt[4]{2}$

Explicación paso a paso: