Whakaoti i te (sqrt{27}-sqrt{1/5})-(sqrt{45}+sqrt{48})

$$( \sqrt { 27 } - \sqrt { \frac { 1 } { 5 } } ) - ( \sqrt { 45 } + \sqrt { 48 } )$$

Aromātai

$$-\frac{16\sqrt{5}}{5}-\sqrt{3}\approx -8.887468336$$

Ngā Hipanga Rongoā Poto

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$3\sqrt{3}-\sqrt{\frac{1}{5}}-\left(\sqrt{45}+\sqrt{48}\right)$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{5}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{5}}.

$$3\sqrt{3}-\frac{\sqrt{1}}{\sqrt{5}}-\left(\sqrt{45}+\sqrt{48}\right)$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$3\sqrt{3}-\frac{1}{\sqrt{5}}-\left(\sqrt{45}+\sqrt{48}\right)$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

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

Ko te pūrua o \sqrt{5} ko 5.

$$3\sqrt{3}-\frac{\sqrt{5}}{5}-\left(\sqrt{45}+\sqrt{48}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 3\sqrt{3} ki te \frac{5}{5}.

$$\frac{5\times 3\sqrt{3}}{5}-\frac{\sqrt{5}}{5}-\left(\sqrt{45}+\sqrt{48}\right)$$

Tā te mea he rite te tauraro o \frac{5\times 3\sqrt{3}}{5} me \frac{\sqrt{5}}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5\times 3\sqrt{3}-\sqrt{5}}{5}-\left(\sqrt{45}+\sqrt{48}\right)$$

Mahia ngā whakarea i roto o 5\times 3\sqrt{3}-\sqrt{5}.

$$\frac{15\sqrt{3}-\sqrt{5}}{5}-\left(\sqrt{45}+\sqrt{48}\right)$$

Tauwehea te 45=3^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 5} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{5}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{15\sqrt{3}-\sqrt{5}}{5}-\left(3\sqrt{5}+\sqrt{48}\right)$$

Tauwehea te 48=4^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{4^{2}\times 3} hei hua o ngā pūtake rua \sqrt{4^{2}}\sqrt{3}. Tuhia te pūtakerua o te 4^{2}.

$$\frac{15\sqrt{3}-\sqrt{5}}{5}-\left(3\sqrt{5}+4\sqrt{3}\right)$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 3\sqrt{5}+4\sqrt{3} ki te \frac{5}{5}.

$$\frac{15\sqrt{3}-\sqrt{5}}{5}-\frac{5\left(3\sqrt{5}+4\sqrt{3}\right)}{5}$$

Tā te mea he rite te tauraro o \frac{15\sqrt{3}-\sqrt{5}}{5} me \frac{5\left(3\sqrt{5}+4\sqrt{3}\right)}{5}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{15\sqrt{3}-\sqrt{5}-5\left(3\sqrt{5}+4\sqrt{3}\right)}{5}$$

Mahia ngā whakarea i roto o 15\sqrt{3}-\sqrt{5}-5\left(3\sqrt{5}+4\sqrt{3}\right).

$$\frac{15\sqrt{3}-\sqrt{5}-15\sqrt{5}-20\sqrt{3}}{5}$$

Mahia ngā tātaitai i roto o 15\sqrt{3}-\sqrt{5}-15\sqrt{5}-20\sqrt{3}.

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