Réitigh sqrt[5]{frac{1/32}:(2/3)^-1}{(1-1/3)2/4+frac{1}{2}}+frac{sqrt{1-frac{16}{25}}}{frac{4}{5}:(frac{15}{2})^1}=

$$\frac { \sqrt[ 5 ] { \frac { 1 } { 32 } } : ( \frac { 2 } { 3 } ) ^ { - 1 } } { ( 1 - \frac { 1 } { 3 } ) \frac { 2 } { 4 } + \frac { 1 } { 2 } } + \frac { \sqrt { 1 - \frac { 16 } { 25 } } } { \frac { 4 } { 5 } : ( \frac { 15 } { 2 } ) ^ { 1 } } =$$

Luacháil

$$\frac{241}{40}=6.025$$

Céimeanna Réitigh

Áirigh \sqrt[5]{\frac{1}{32}} agus faigh \frac{1}{2}.

$$\frac{\frac{\frac{1}{2}}{\left(\frac{2}{3}\right)^{-1}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Ríomh cumhacht \frac{2}{3} de -1 agus faigh \frac{3}{2}.

$$\frac{\frac{\frac{1}{2}}{\frac{3}{2}}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Roinn \frac{1}{2} faoi \frac{3}{2} trí \frac{1}{2} a mhéadú faoi dheilín \frac{3}{2}.

$$\frac{\frac{1}{2}\times \frac{2}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Méadaigh \frac{1}{2} agus \frac{2}{3} chun \frac{1}{3} a fháil.

$$\frac{\frac{1}{3}}{\left(1-\frac{1}{3}\right)\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Dealaigh \frac{1}{3} ó 1 chun \frac{2}{3} a fháil.

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{2}{4}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Laghdaigh an codán \frac{2}{4} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$\frac{\frac{1}{3}}{\frac{2}{3}\times \frac{1}{2}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Méadaigh \frac{2}{3} agus \frac{1}{2} chun \frac{1}{3} a fháil.

$$\frac{\frac{1}{3}}{\frac{1}{3}+\frac{1}{2}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Suimigh \frac{1}{3} agus \frac{1}{2} chun \frac{5}{6} a fháil.

$$\frac{\frac{1}{3}}{\frac{5}{6}}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Roinn \frac{1}{3} faoi \frac{5}{6} trí \frac{1}{3} a mhéadú faoi dheilín \frac{5}{6}.

$$\frac{1}{3}\times \frac{6}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Méadaigh \frac{1}{3} agus \frac{6}{5} chun \frac{2}{5} a fháil.

$$\frac{2}{5}+\frac{\sqrt{1-\frac{16}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Dealaigh \frac{16}{25} ó 1 chun \frac{9}{25} a fháil.

$$\frac{2}{5}+\frac{\sqrt{\frac{9}{25}}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Athscríobh fréamh cearnach na roinnte \frac{9}{25} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{9}}{\sqrt{25}}. Tóg fréamh chearnach an uimhreora agus an ainmneora.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\left(\frac{15}{2}\right)^{1}}}$$

Ríomh cumhacht \frac{15}{2} de 1 agus faigh \frac{15}{2}.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{\frac{4}{5}}{\frac{15}{2}}}$$

Roinn \frac{4}{5} faoi \frac{15}{2} trí \frac{4}{5} a mhéadú faoi dheilín \frac{15}{2}.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{4}{5}\times \frac{2}{15}}$$

Méadaigh \frac{4}{5} agus \frac{2}{15} chun \frac{8}{75} a fháil.

$$\frac{2}{5}+\frac{\frac{3}{5}}{\frac{8}{75}}$$

Roinn \frac{3}{5} faoi \frac{8}{75} trí \frac{3}{5} a mhéadú faoi dheilín \frac{8}{75}.

$$\frac{2}{5}+\frac{3}{5}\times \frac{75}{8}$$

Méadaigh \frac{3}{5} agus \frac{75}{8} chun \frac{45}{8} a fháil.

$$\frac{2}{5}+\frac{45}{8}$$

Suimigh \frac{2}{5} agus \frac{45}{8} chun \frac{241}{40} a fháil.

$$\frac{241}{40}$$

Fachtóirigh

$$\frac{241}{2 ^ {3} \cdot 5} = 6\frac{1}{40} = 6.025$$