Datrys 12/9+sqrt{7}

$$\frac { 12 } { 9 + \sqrt { 7 } }$$

Enrhifo

$$\frac{54-6\sqrt{7}}{37}\approx 1.030418706$$

Camau Ateb

Mae'n rhesymoli enwadur \frac{12}{9+\sqrt{7}} drwy luosi'r rhifiadur a'r enwadur â 9-\sqrt{7}.

$$\frac{12\left(9-\sqrt{7}\right)}{\left(9+\sqrt{7}\right)\left(9-\sqrt{7}\right)}$$

Ystyriwch \left(9+\sqrt{7}\right)\left(9-\sqrt{7}\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{12\left(9-\sqrt{7}\right)}{9^{2}-\left(\sqrt{7}\right)^{2}}$$

Sgwâr 9. Sgwâr \sqrt{7}.

$$\frac{12\left(9-\sqrt{7}\right)}{81-7}$$

Tynnu 7 o 81 i gael 74.

$$\frac{12\left(9-\sqrt{7}\right)}{74}$$

Rhannu 12\left(9-\sqrt{7}\right) â 74 i gael \frac{6}{37}\left(9-\sqrt{7}\right).

$$\frac{6}{37}\left(9-\sqrt{7}\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi \frac{6}{37} â 9-\sqrt{7}.

$$\frac{6}{37}\times 9+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Mynegwch \frac{6}{37}\times 9 fel ffracsiwn unigol.

$$\frac{6\times 9}{37}+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Lluosi 6 a 9 i gael 54.

$$\frac{54}{37}+\frac{6}{37}\left(-1\right)\sqrt{7}$$

Lluosi \frac{6}{37} a -1 i gael -\frac{6}{37}.

$$\frac{54}{37}-\frac{6}{37}\sqrt{7}$$