Réitigh frac{{left(sqrt{3}+1+sqrt{3}-1right)}^2}{{left(sqrt{3}+1right)}^2-{left(sqrt{3}-1right)}^2}

$$\frac{ { \left( \sqrt{ 3 } +1+ \sqrt{ 3 } -1 \right) }^{ 2 } }{ { \left( \sqrt{ 3 } +1 \right) }^{ 2 } - { \left( \sqrt{ 3 } -1 \right) }^{ 2 } }$$

Luacháil

$$\sqrt{3}\approx 1.732050808$$

Céimeanna Réitigh

Comhcheangail \sqrt{3} agus \sqrt{3} chun 2\sqrt{3} a fháil.

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Dealaigh 1 ó 1 chun 0 a fháil.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Fairsingigh \left(2\sqrt{3}\right)^{2}

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Méadaigh 4 agus 3 chun 12 a fháil.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{3}+1\right)^{2} a leathnú.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Suimigh 3 agus 1 chun 4 a fháil.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{3}-1\right)^{2} a leathnú.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Suimigh 3 agus 1 chun 4 a fháil.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Chun an mhalairt ar 4-2\sqrt{3} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

Dealaigh 4 ó 4 chun 0 a fháil.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Comhcheangail 2\sqrt{3} agus 2\sqrt{3} chun 4\sqrt{3} a fháil.

$$\frac{12}{4\sqrt{3}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3} chun ainmneoir \frac{12}{4\sqrt{3}} a thiontú in uimhir chóimheasta.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12\sqrt{3}}{4\times 3}$$

Cealaigh 3\times 4 mar uimhreoir agus ainmneoir.

$$\sqrt{3}$$

Fairsingigh

$$\sqrt{3} = 1.732050808$$

Céimeanna Réitigh

Comhcheangail \sqrt{3} agus \sqrt{3} chun 2\sqrt{3} a fháil.

$$\frac{\left(2\sqrt{3}+1-1\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Dealaigh 1 ó 1 chun 0 a fháil.

$$\frac{\left(2\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Fairsingigh \left(2\sqrt{3}\right)^{2}

$$\frac{2^{2}\left(\sqrt{3}\right)^{2}}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Ríomh cumhacht 2 de 2 agus faigh 4.

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

Is é 3 uimhir chearnach \sqrt{3}.

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

Méadaigh 4 agus 3 chun 12 a fháil.

$$\frac{12}{\left(\sqrt{3}+1\right)^{2}-\left(\sqrt{3}-1\right)^{2}}$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(\sqrt{3}+1\right)^{2} a leathnú.

$$\frac{12}{\left(\sqrt{3}\right)^{2}+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12}{3+2\sqrt{3}+1-\left(\sqrt{3}-1\right)^{2}}$$

Suimigh 3 agus 1 chun 4 a fháil.

$$\frac{12}{4+2\sqrt{3}-\left(\sqrt{3}-1\right)^{2}}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(\sqrt{3}-1\right)^{2} a leathnú.

$$\frac{12}{4+2\sqrt{3}-\left(\left(\sqrt{3}\right)^{2}-2\sqrt{3}+1\right)}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12}{4+2\sqrt{3}-\left(3-2\sqrt{3}+1\right)}$$

Suimigh 3 agus 1 chun 4 a fháil.

$$\frac{12}{4+2\sqrt{3}-\left(4-2\sqrt{3}\right)}$$

Chun an mhalairt ar 4-2\sqrt{3} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$\frac{12}{4+2\sqrt{3}-4+2\sqrt{3}}$$

Dealaigh 4 ó 4 chun 0 a fháil.

$$\frac{12}{2\sqrt{3}+2\sqrt{3}}$$

Comhcheangail 2\sqrt{3} agus 2\sqrt{3} chun 4\sqrt{3} a fháil.

$$\frac{12}{4\sqrt{3}}$$

Iolraigh an t-uimhreoir agus an t-ainmneoir faoi \sqrt{3} chun ainmneoir \frac{12}{4\sqrt{3}} a thiontú in uimhir chóimheasta.

$$\frac{12\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

Is é 3 uimhir chearnach \sqrt{3}.

$$\frac{12\sqrt{3}}{4\times 3}$$

Cealaigh 3\times 4 mar uimhreoir agus ainmneoir.

$$\sqrt{3}$$