Question

Alguien me puede explicar esto

Answer 1

$a)\quad 6 \sqrt{ \dfrac{8}{9}}-7 \sqrt{ \dfrac{200}{196} }+45 \sqrt{ \dfrac{18}{225}}= \quad distribu\'imos \ las \ ra\'ices$

$6 \dfrac{ \sqrt{8}}{ \sqrt{9}}}-7 \dfrac{ \sqrt{200}}{ \sqrt{196}} }+45 \dfrac{ \sqrt{18}}{ \sqrt{225}}= \quad resolvemos \\ \\ \\ \\ 6 \dfrac{ \sqrt{2^3}}{ \sqrt{3^2}}}-7 \dfrac{ \sqrt{2^3*5^2}}{ \sqrt{2^2*7^2}} }+45 \dfrac{ \sqrt{2*3^2}}{ \sqrt{3^2*5^2}}}= \\ \\ \\ 6 \dfrac{2\sqrt{2}}{ 3}}-7 \dfrac{2*5 \sqrt{2}}{ 2*7} }+45 \dfrac{3 \sqrt{2}}{3*5}}= \\ \\ \\ 6 \dfrac{2\sqrt{2}}{ 3}}-7 \dfrac{10 \sqrt{2}}{14} }+45 \dfrac{3 \sqrt{2}}{15}}=$


$\not6^2 \dfrac{2\sqrt{2}}{ \not3^1}}-\not7^1 \dfrac{10 \sqrt{2}}{\not1\not4^2} }+\not4\not5^3 \dfrac{3 \sqrt{2}}{\not1\not5}}=\quad simplificamos \\ \\ \\2*2\sqrt{2}- \dfrac{10 \sqrt{2}}{2} }+3*3 \sqrt{2}= \\ \\ \\ 4\sqrt{2}- 5 \sqrt{2}+9\sqrt{2}= (4-5+9)* \sqrt{2}= \boxed{ \boxed{8 \sqrt{2} }}$


Espero que te sirva, salu2!!!!