Issolvi 12/9+sqrt{7}

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

Evalwa

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

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{12}{9+\sqrt{7}} billi timmultiplika in-numeratur u d-denominatur mill-9-\sqrt{7}.

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

Ikkunsidra li \left(9+\sqrt{7}\right)\left(9-\sqrt{7}\right). Il-multiplikazzjoni tista' tiġi ttrasformata fid-differenza tal-kwadrati li jużaw ir-regola: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ikkwadra 9. Ikkwadra \sqrt{7}.

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

Naqqas 7 minn 81 biex tikseb 74.

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

Iddividi 12\left(9-\sqrt{7}\right) b'74 biex tikseb\frac{6}{37}\left(9-\sqrt{7}\right).

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

Uża l-propjetà distributtiva biex timmultiplika \frac{6}{37} b'9-\sqrt{7}.

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

Esprimi \frac{6}{37}\times 9 bħala frazzjoni waħda.

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

Immultiplika 6 u 9 biex tikseb 54.

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

Immultiplika \frac{6}{37} u -1 biex tikseb -\frac{6}{37}.

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