Whakaoti i te 1/4sqrt{80}-1/16sqrt{63}-1/9sqrt{180}

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

Aromātai

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

Ngā Upane Otinga

Tauwehea te 80=4^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 5} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{5}. Tuhia te pūtakerua o te 4^{2}.

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

Me whakakore te 4 me te 4.

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

Tauwehea te 63=3^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 7} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{7}. Tuhia te pūtakerua o te 3^{2}.

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

Tuhia te -\frac{1}{16}\times 3 hei hautanga kotahi.

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

Ka taea te hautanga \frac{-3}{16} te tuhi anō ko -\frac{3}{16} mā te tango i te tohu tōraro.

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

Tauwehea te 180=6^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{6^{2}\times 5} hei hua o ngā pūtake rua \sqrt{6^{2}}\sqrt{5}. Tuhia te pūtakerua o te 6^{2}.

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

Tuhia te -\frac{1}{9}\times 6 hei hautanga kotahi.

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

Whakahekea te hautanga \frac{-6}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

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

Pahekotia te \sqrt{5} me -\frac{2}{3}\sqrt{5}, ka \frac{1}{3}\sqrt{5}.

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

Tauwehe

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