Whakaoti i te frac{sqrt{3}}{sqrt{5}}-frac{sqrt{5}+sqrt{30}}{sqrt{2}}

$$\frac { \sqrt { 3 } } { \sqrt { 5 } } - \frac { \sqrt { 5 } + \sqrt { 30 } } { \sqrt { 2 } }$$

Aromātai

$$-\frac{\sqrt{10}}{2}-\frac{4\sqrt{15}}{5}\approx -4.679525507$$

Ngā Hipanga Rongoā Poto

Whakangāwaritia te tauraro o \frac{\sqrt{3}}{\sqrt{5}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{5}.

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

Ko te pūrua o \sqrt{5} ko 5.

$$\frac{\sqrt{3}\sqrt{5}}{5}-\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}}$$

Hei whakarea \sqrt{3} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{15}}{5}-\frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{5}+\sqrt{30}}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

$$\frac{\sqrt{15}}{5}-\frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{\sqrt{15}}{5}-\frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5 me 2 ko 10. Whakareatia \frac{\sqrt{15}}{5} ki te \frac{2}{2}. Whakareatia \frac{\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{2} ki te \frac{5}{5}.

$$\frac{2\sqrt{15}}{10}-\frac{5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10}$$

Tā te mea he rite te tauraro o \frac{2\sqrt{15}}{10} me \frac{5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{2\sqrt{15}-5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}}{10}$$

Mahia ngā whakarea i roto o 2\sqrt{15}-5\left(\sqrt{5}+\sqrt{30}\right)\sqrt{2}.

$$\frac{2\sqrt{15}-5\sqrt{10}-10\sqrt{15}}{10}$$

Mahia ngā tātaitai i roto o 2\sqrt{15}-5\sqrt{10}-10\sqrt{15}.

$$\frac{-8\sqrt{15}-5\sqrt{10}}{10}$$