Réitigh (sqrt{48}-sqrt{50}+sqrt{48}-sqrt{45})-(sqrt{50}-sqrt{45})^2

$$( \sqrt { 48 } - \sqrt { 50 } + \sqrt { 48 } - \sqrt { 45 } ) - ( \sqrt { 50 } - \sqrt { 45 } ) ^ { 2 }$$

Luacháil

$$8\sqrt{3}+30\sqrt{10}-3\sqrt{5}-5\sqrt{2}-95\approx -0.054535479$$

Céimeanna Réitigh

Fachtóirigh 48=4^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{3}. Tóg fréamh chearnach 4^{2}.

$$4\sqrt{3}-\sqrt{50}+\sqrt{48}-\sqrt{45}-\left(\sqrt{50}-\sqrt{45}\right)^{2}$$

Fachtóirigh 50=5^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{5^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{5^{2}}\sqrt{2}. Tóg fréamh chearnach 5^{2}.

$$4\sqrt{3}-5\sqrt{2}+\sqrt{48}-\sqrt{45}-\left(\sqrt{50}-\sqrt{45}\right)^{2}$$

Fachtóirigh 48=4^{2}\times 3. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 3} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{3}. Tóg fréamh chearnach 4^{2}.

$$4\sqrt{3}-5\sqrt{2}+4\sqrt{3}-\sqrt{45}-\left(\sqrt{50}-\sqrt{45}\right)^{2}$$

Comhcheangail 4\sqrt{3} agus 4\sqrt{3} chun 8\sqrt{3} a fháil.

$$8\sqrt{3}-5\sqrt{2}-\sqrt{45}-\left(\sqrt{50}-\sqrt{45}\right)^{2}$$

Fachtóirigh 45=3^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{5}. Tóg fréamh chearnach 3^{2}.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(\sqrt{50}-\sqrt{45}\right)^{2}$$

Fachtóirigh 50=5^{2}\times 2. Athscríobh fréamh cearnach an toraidh \sqrt{5^{2}\times 2} mar thoradh na bhfréamhacha cearnacha \sqrt{5^{2}}\sqrt{2}. Tóg fréamh chearnach 5^{2}.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(5\sqrt{2}-\sqrt{45}\right)^{2}$$

Fachtóirigh 45=3^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{5}. Tóg fréamh chearnach 3^{2}.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(5\sqrt{2}-3\sqrt{5}\right)^{2}$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(5\sqrt{2}-3\sqrt{5}\right)^{2} a leathnú.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(25\left(\sqrt{2}\right)^{2}-30\sqrt{2}\sqrt{5}+9\left(\sqrt{5}\right)^{2}\right)$$

Is é 2 uimhir chearnach \sqrt{2}.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(25\times 2-30\sqrt{2}\sqrt{5}+9\left(\sqrt{5}\right)^{2}\right)$$

Méadaigh 25 agus 2 chun 50 a fháil.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(50-30\sqrt{2}\sqrt{5}+9\left(\sqrt{5}\right)^{2}\right)$$

Iolraigh na huimhreacha faoin bhfréamh cearnach chun \sqrt{2} agus \sqrt{5} a iolrú.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(50-30\sqrt{10}+9\left(\sqrt{5}\right)^{2}\right)$$

Is é 5 uimhir chearnach \sqrt{5}.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(50-30\sqrt{10}+9\times 5\right)$$

Méadaigh 9 agus 5 chun 45 a fháil.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(50-30\sqrt{10}+45\right)$$

Suimigh 50 agus 45 chun 95 a fháil.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-\left(95-30\sqrt{10}\right)$$

Chun an mhalairt ar 95-30\sqrt{10} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$8\sqrt{3}-5\sqrt{2}-3\sqrt{5}-95+30\sqrt{10}$$