Whakaoti i te (1-sqrt{18})(sqrt{2}+1/sqrt{2})

$$( 1 - \sqrt { 18 } ) ( \sqrt { 2 } + \frac { 1 } { \sqrt { 2 } } )$$

Aromātai

$$\frac{3\left(\sqrt{2}-6\right)}{2}\approx -6.878679656$$

Ngā Upane Otinga

Tauwehea te 18=3^{2}\times 2. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 2} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{2}. Tuhia te pūtakerua o te 3^{2}.

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

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

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

Ko te pūrua o \sqrt{2} ko 2.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te 1-3\sqrt{2} ki te \frac{3}{2}.

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

Tuhia te -3\times \frac{3}{2} hei hautanga kotahi.

$$\left(\frac{3}{2}+\frac{-3\times 3}{2}\sqrt{2}\right)\sqrt{2}$$

Whakareatia te -3 ki te 3, ka -9.

$$\left(\frac{3}{2}+\frac{-9}{2}\sqrt{2}\right)\sqrt{2}$$

Ka taea te hautanga \frac{-9}{2} te tuhi anō ko -\frac{9}{2} mā te tango i te tohu tōraro.

$$\left(\frac{3}{2}-\frac{9}{2}\sqrt{2}\right)\sqrt{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{3}{2}-\frac{9}{2}\sqrt{2} ki te \sqrt{2}.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\sqrt{2}\sqrt{2}$$

Whakareatia te \sqrt{2} ki te \sqrt{2}, ka 2.

$$\frac{3}{2}\sqrt{2}-\frac{9}{2}\times 2$$

Me whakakore te 2 me te 2.

$$\frac{3}{2}\sqrt{2}-9$$

Tauwehe

$$\frac{3 {(\sqrt{2} - 6)}}{2} = -6.878679656440358$$