Réitigh sqrt{56/149}*12/3-(3/5)^2=

$$\sqrt { \frac { 56 } { 149 } } \cdot \frac { 12 } { 3 } - ( \frac { 3 } { 5 } ) ^ { 2 } =$$

Luacháil

$$\frac{8\sqrt{2086}}{149}-\frac{9}{25}\approx 2.092228134$$

Céimeanna gearra réitigh

Athscríobh fréamh cearnach na roinnte \sqrt{\frac{56}{149}} mar roinnt na bhfréamhacha cearnacha \frac{\sqrt{56}}{\sqrt{149}}.

$$\frac{\sqrt{56}}{\sqrt{149}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Fachtóirigh 56=2^{2}\times 14. Athscríobh fréamh cearnach an toraidh \sqrt{2^{2}\times 14} mar thoradh na bhfréamhacha cearnacha \sqrt{2^{2}}\sqrt{14}. Tóg fréamh chearnach 2^{2}.

$$\frac{2\sqrt{14}}{\sqrt{149}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{149} chun ainmneoir \frac{2\sqrt{14}}{\sqrt{149}} a thiontú in uimhir chóimheasta.

$$\frac{2\sqrt{14}\sqrt{149}}{\left(\sqrt{149}\right)^{2}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Is é 149 uimhir chearnach \sqrt{149}.

$$\frac{2\sqrt{14}\sqrt{149}}{149}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{14} agus \sqrt{149} a iolrú.

$$\frac{2\sqrt{2086}}{149}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Roinn 12 faoi 3 chun 4 a fháil.

$$\frac{2\sqrt{2086}}{149}\times 4-\left(\frac{3}{5}\right)^{2}$$

Scríobh \frac{2\sqrt{2086}}{149}\times 4 mar chodán aonair.

$$\frac{2\sqrt{2086}\times 4}{149}-\left(\frac{3}{5}\right)^{2}$$

Ríomh cumhacht \frac{3}{5} de 2 agus faigh \frac{9}{25}.

$$\frac{2\sqrt{2086}\times 4}{149}-\frac{9}{25}$$

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 149 agus 25 ná 3725. Méadaigh \frac{2\sqrt{2086}\times 4}{149} faoi \frac{25}{25}. Méadaigh \frac{9}{25} faoi \frac{149}{149}.

$$\frac{25\times 2\sqrt{2086}\times 4}{3725}-\frac{9\times 149}{3725}$$

Tá an t-ainmneoir céanna ag \frac{25\times 2\sqrt{2086}\times 4}{3725} agus \frac{9\times 149}{3725} agus, mar sin, is féidir iad a dhealú trína n-uimhreoirí a dhealú.

$$\frac{25\times 2\sqrt{2086}\times 4-9\times 149}{3725}$$

Déan iolrúcháin in 25\times 2\sqrt{2086}\times 4-9\times 149.

$$\frac{200\sqrt{2086}-1341}{3725}$$

Fachtóirigh

$$\frac{200 \sqrt{2086} - 1341}{3725} = 2.092228133512856$$