Question

ALGUIEN QUE AYUDE A RESOLVER

√1/32 − √1/8÷ √1/4

10 PUNTOS

Answer 1

La resolución del ejercicio es la siguiente:

$\sqrt{\frac{1}{32}}-\frac{\sqrt{\frac{1}{8}}}{\sqrt{\frac{1}{4}}}=-\frac{3\sqrt{2}}{8}\quad$

$\sqrt{\frac{1}{32}}-\frac{\sqrt{\frac{1}{8}}}{\sqrt{\frac{1}{4}}}$

Simplificando el primer termino

$\sqrt{\frac{1}{32}} =\frac{\sqrt{1}}{\sqrt{32}}=\frac{\sqrt{1}}{4\sqrt{2}}=\frac{1}{4\sqrt{2}}$

Simplificando el segundo termino

$\frac{\sqrt{\frac{1}{8}}}{\sqrt{\frac{1}{4}}}=\frac{\sqrt{\frac{1}{8}}}{\frac{1}{2}}=\frac{\sqrt{\frac{1}{8}}}{\frac{1}{2}}=\frac{1\cdot \:2}{2\sqrt{2}\cdot \:1}=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$

Resta de ambos términos simplificados

$\sqrt{\frac{1}{32}}-\frac{\sqrt{\frac{1}{8}}}{\sqrt{\frac{1}{4}}}=\frac{1}{4\sqrt{2}}-\frac{1}{\sqrt{2}}=\frac{1}{4\sqrt{2}}-\frac{4}{4\sqrt{2}}=\frac{1}{4\sqrt{2}}-\frac{4}{4\sqrt{2}}=\frac{-3}{4\sqrt{2}}=-\frac{3}{4\sqrt{2}}=-\frac{3\sqrt{2}}{4\sqrt{2}\sqrt{2}}=-\frac{3\sqrt{2}}{8}$

Entonces quedaría que: $\sqrt{\frac{1}{32}}-\frac{\sqrt{\frac{1}{8}}}{\sqrt{\frac{1}{4}}}=-\frac{3\sqrt{2}}{8}\quad$