Question

Hola en estos momentos no entiendo este ejercicio:
√2(2√1/2-√5/2) me podrian ayudar?

Answer 1

Sabemos que:
$\sqrt{ab}=\,\sqrt{a}\sqrt{b}\,\textsf{y que:}\\\sqrt{\frac{a}{b}}=\,\frac{\sqrt{a}}{\sqrt{b}}\\ \sqrt{a}=a^{\frac{1}{2}}$
Entonces:
$\sqrt{2}(2\sqrt{\frac{1}{2}}-\sqrt{\frac{5}{2}})=\\2^{1/2}[(2(1/2)^{1/2})-(5/2)^{1/2})]=\\2[2^{1/2}[1/2]^{1/2}-(2^{1/2}[5/2]^{1/2})=\\2[2(1/2)]^{1/2}-(2[5/2])^{1/2}=\\2[1]^{1/2}-5^{1/2}=\\2-\sqrt{5}$
Saludos.