Whakaoti i te sqrt{1-(frac{3sqrt{7}}{14})^2}

$$\sqrt { 1 - ( \frac { 3 \sqrt { 7 } } { 14 } ) ^ { 2 } }$$

Aromātai

$$\frac{\sqrt{133}}{14}\approx 0.823754471$$

Ngā Upane Otinga

Kia whakarewa i te \frac{3\sqrt{7}}{14} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\sqrt{1-\frac{\left(3\sqrt{7}\right)^{2}}{14^{2}}}$$

Whakarohaina te \left(3\sqrt{7}\right)^{2}.

$$\sqrt{1-\frac{3^{2}\left(\sqrt{7}\right)^{2}}{14^{2}}}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$\sqrt{1-\frac{9\left(\sqrt{7}\right)^{2}}{14^{2}}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\sqrt{1-\frac{9\times 7}{14^{2}}}$$

Whakareatia te 9 ki te 7, ka 63.

$$\sqrt{1-\frac{63}{14^{2}}}$$

Tātaihia te 14 mā te pū o 2, kia riro ko 196.

$$\sqrt{1-\frac{63}{196}}$$

Whakahekea te hautanga \frac{63}{196} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\sqrt{1-\frac{9}{28}}$$

Tangohia te \frac{9}{28} i te 1, ka \frac{19}{28}.

$$\sqrt{\frac{19}{28}}$$

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{19}{28}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{19}}{\sqrt{28}}.

$$\frac{\sqrt{19}}{\sqrt{28}}$$

Tauwehea te 28=2^{2}\times 7. Tuhia anō te pūtake rua o te hua \sqrt{2^{2}\times 7} hei hua o ngā pūtake rua \sqrt{2^{2}}\sqrt{7}. Tuhia te pūtakerua o te 2^{2}.

$$\frac{\sqrt{19}}{2\sqrt{7}}$$

Whakangāwaritia te tauraro o \frac{\sqrt{19}}{2\sqrt{7}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{7}.

$$\frac{\sqrt{19}\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}$$

Ko te pūrua o \sqrt{7} ko 7.

$$\frac{\sqrt{19}\sqrt{7}}{2\times 7}$$

Hei whakarea \sqrt{19} me \sqrt{7}, whakareatia ngā tau i raro i te pūtake rua.

$$\frac{\sqrt{133}}{2\times 7}$$

Whakareatia te 2 ki te 7, ka 14.

$$\frac{\sqrt{133}}{14}$$