Réitigh =(3/sqrt{3})^2-2(3/sqrt{3})(5/sqrt{2})+(5/sqrt{2})^2

$$= ( \frac { 3 } { \sqrt { 3 } } ) ^ { 2 } - 2 ( \frac { 3 } { \sqrt { 3 } } ) ( \frac { 5 } { \sqrt { 2 } } ) + ( \frac { 5 } { \sqrt { 2 } } ) ^ { 2 }$$

Luacháil

$$\frac{31}{2}-5\sqrt{6}\approx 3.252551286$$

Céimeanna Réitigh

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3} chun ainmneoir \frac{3}{\sqrt{3}} a thiontú in uimhir chóimheasta.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Cealaigh 3 agus 3.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3} chun ainmneoir \frac{3}{\sqrt{3}} a thiontú in uimhir chóimheasta.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Cealaigh 3 agus 3.

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

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{5}{\sqrt{2}} a thiontú in uimhir chóimheasta.

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

Is é 2 uimhir chearnach \sqrt{2}.

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

Cealaigh 2 agus 2.

$$3-5\sqrt{2}\sqrt{3}+\left(\frac{5}{\sqrt{2}}\right)^{2}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{2} chun ainmneoir \frac{5}{\sqrt{2}} a thiontú in uimhir chóimheasta.

$$3-5\sqrt{2}\sqrt{3}+\left(\frac{5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}$$

Is é 2 uimhir chearnach \sqrt{2}.

$$3-5\sqrt{2}\sqrt{3}+\left(\frac{5\sqrt{2}}{2}\right)^{2}$$

Chun \frac{5\sqrt{2}}{2} a iolrú i gcumhacht, iolraigh an t-uimhreoir agus an t-ainmneoir araon i gcumhacht agus déan iad a roinnt ansin.

$$3-5\sqrt{2}\sqrt{3}+\frac{\left(5\sqrt{2}\right)^{2}}{2^{2}}$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{3} a iolrú.

$$3-5\sqrt{6}+\frac{\left(5\sqrt{2}\right)^{2}}{2^{2}}$$

Fairsingigh \left(5\sqrt{2}\right)^{2}

$$3-5\sqrt{6}+\frac{5^{2}\left(\sqrt{2}\right)^{2}}{2^{2}}$$

Ríomh cumhacht 5 de 2 agus faigh 25.

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

Is é 2 uimhir chearnach \sqrt{2}.

$$3-5\sqrt{6}+\frac{25\times 2}{2^{2}}$$

Méadaigh 25 agus 2 chun 50 a fháil.

$$3-5\sqrt{6}+\frac{50}{2^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

$$3-5\sqrt{6}+\frac{50}{4}$$

Laghdaigh an codán \frac{50}{4} chuig na téarmaí is ísle trí 2 a bhaint agus a chealú.

$$3-5\sqrt{6}+\frac{25}{2}$$

Suimigh 3 agus \frac{25}{2} chun \frac{31}{2} a fháil.

$$\frac{31}{2}-5\sqrt{6}$$