Réitigh 1/4sqrt{80}-1/16sqrt{63}-1/9sqrt{180}

$$\frac { 1 } { 4 } \sqrt { 80 } - \frac { 1 } { 16 } \sqrt { 63 } - \frac { 1 } { 9 } \sqrt { 180 }$$

Luacháil

$$\frac{\sqrt{5}}{3}-\frac{3\sqrt{7}}{16}\approx 0.249277622$$

Céimeanna Réitigh

Fachtóirigh 80=4^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{4^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{4^{2}}\sqrt{5}. Tóg fréamh chearnach 4^{2}.

$$\frac{1}{4}\times 4\sqrt{5}-\frac{1}{16}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

Cealaigh 4 agus 4.

$$\sqrt{5}-\frac{1}{16}\sqrt{63}-\frac{1}{9}\sqrt{180}$$

Fachtóirigh 63=3^{2}\times 7. Athscríobh fréamh cearnach an toraidh \sqrt{3^{2}\times 7} mar thoradh na bhfréamhacha cearnacha \sqrt{3^{2}}\sqrt{7}. Tóg fréamh chearnach 3^{2}.

$$\sqrt{5}-\frac{1}{16}\times 3\sqrt{7}-\frac{1}{9}\sqrt{180}$$

Scríobh -\frac{1}{16}\times 3 mar chodán aonair.

$$\sqrt{5}+\frac{-3}{16}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

Is féidir an codán \frac{-3}{16} a athscríobh mar -\frac{3}{16} ach an comhartha diúltach a bhaint.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{1}{9}\sqrt{180}$$

Fachtóirigh 180=6^{2}\times 5. Athscríobh fréamh cearnach an toraidh \sqrt{6^{2}\times 5} mar thoradh na bhfréamhacha cearnacha \sqrt{6^{2}}\sqrt{5}. Tóg fréamh chearnach 6^{2}.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{1}{9}\times 6\sqrt{5}$$

Scríobh -\frac{1}{9}\times 6 mar chodán aonair.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}+\frac{-6}{9}\sqrt{5}$$

Laghdaigh an codán \frac{-6}{9} chuig na téarmaí is ísle trí 3 a bhaint agus a chealú.

$$\sqrt{5}-\frac{3}{16}\sqrt{7}-\frac{2}{3}\sqrt{5}$$

Comhcheangail \sqrt{5} agus -\frac{2}{3}\sqrt{5} chun \frac{1}{3}\sqrt{5} a fháil.

$$\frac{1}{3}\sqrt{5}-\frac{3}{16}\sqrt{7}$$

Fachtóirigh

$$\frac{16 \sqrt{5} - 9 \sqrt{7}}{48} = 0.2492776216753192$$