Datrys (2sqrt{2}-1)^2-(1+sqrt{3})*(sqrt{2}-sqrt{6})

$$( 2 \sqrt { 2 } - 1 ) ^ { 2 } - ( 1 + \sqrt { 3 } ) \times ( \sqrt { 2 } - \sqrt { 6 } )$$

Enrhifo

$$9-2\sqrt{2}\approx 6.171572875$$

Camau Ateb

Defnyddio'r theorem binomaidd \left(a-b\right)^{2}=a^{2}-2ab+b^{2} i ehangu'r \left(2\sqrt{2}-1\right)^{2}.

$$4\left(\sqrt{2}\right)^{2}-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Sgwâr \sqrt{2} yw 2.

$$4\times 2-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Lluosi 4 a 2 i gael 8.

$$8-4\sqrt{2}+1-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Adio 8 a 1 i gael 9.

$$9-4\sqrt{2}-\left(1+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{6}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 1+\sqrt{3} â \sqrt{2}-\sqrt{6}.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{3}\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

I luosi \sqrt{3} a \sqrt{2}, dylid lluosi'r rhifau dan yr ail isradd.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{6}+\sqrt{6}-\sqrt{3}\sqrt{6}\right)$$

Cyfuno -\sqrt{6} a \sqrt{6} i gael 0.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{6}\right)$$

Ffactora 6=3\times 2. Ailysgrifennu ail isradd y lluoswm \sqrt{3\times 2} fel lluoswm ail israddau \sqrt{3}\sqrt{2}.

$$9-4\sqrt{2}-\left(\sqrt{2}-\sqrt{3}\sqrt{3}\sqrt{2}\right)$$

Lluosi \sqrt{3} a \sqrt{3} i gael 3.

$$9-4\sqrt{2}-\left(\sqrt{2}-3\sqrt{2}\right)$$

Cyfuno \sqrt{2} a -3\sqrt{2} i gael -2\sqrt{2}.

$$9-4\sqrt{2}-\left(-2\sqrt{2}\right)$$

Gwrthwyneb -2\sqrt{2} yw 2\sqrt{2}.

$$9-4\sqrt{2}+2\sqrt{2}$$

Cyfuno -4\sqrt{2} a 2\sqrt{2} i gael -2\sqrt{2}.

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