Whakaoti i te 4/(sqrt{3)^2}+1/(sqrt{3/2)^2}-(1/sqrt{2})^2

$$\frac { 4 } { ( \sqrt { 3 } ) ^ { 2 } } + \frac { 1 } { ( \frac { \sqrt { 3 } } { 2 } ) ^ { 2 } } - ( \frac { 1 } { \sqrt { 2 } } ) ^ { 2 }$$

Aromātai

$$\frac{13}{6}\approx 2.166666667$$

Ngā Upane Otinga

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4}{3}+\frac{1}{\left(\frac{\sqrt{3}}{2}\right)^{2}}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Kia whakarewa i te \frac{\sqrt{3}}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{4}{3}+\frac{1}{\frac{\left(\sqrt{3}\right)^{2}}{2^{2}}}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Whakawehe 1 ki te \frac{\left(\sqrt{3}\right)^{2}}{2^{2}} mā te whakarea 1 ki te tau huripoki o \frac{\left(\sqrt{3}\right)^{2}}{2^{2}}.

$$\frac{4}{3}+\frac{2^{2}}{\left(\sqrt{3}\right)^{2}}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{4}{3}+\frac{4}{\left(\sqrt{3}\right)^{2}}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{4}{3}+\frac{4}{3}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Tāpirihia te \frac{4}{3} ki te \frac{4}{3}, ka \frac{8}{3}.

$$\frac{8}{3}-\left(\frac{1}{\sqrt{2}}\right)^{2}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{2}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{2}.

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

Ko te pūrua o \sqrt{2} ko 2.

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

Kia whakarewa i te \frac{\sqrt{2}}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Ko te pūrua o \sqrt{2} ko 2.

$$\frac{8}{3}-\frac{2}{2^{2}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{8}{3}-\frac{2}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{8}{3}-\frac{1}{2}$$

Tangohia te \frac{1}{2} i te \frac{8}{3}, ka \frac{13}{6}.

$$\frac{13}{6}$$

Tauwehe

$$\frac{13}{2 \cdot 3} = 2\frac{1}{6} = 2.1666666666666665$$