Issolvi frac{3sqrt{10}}{2+sqrt{10}}

$$\frac{ 3 \sqrt{ 10 } }{ 2+ \sqrt{ 10 } }$$

Evalwa

$$5-\sqrt{10}\approx 1.83772234$$

Passi tas-Soluzzjonijiet

Irrazzjonalizza d-denominatur tal-\frac{3\sqrt{10}}{2+\sqrt{10}} billi timmultiplika in-numeratur u d-denominatur mill-2-\sqrt{10}.

$$\frac{3\sqrt{10}\left(2-\sqrt{10}\right)}{\left(2+\sqrt{10}\right)\left(2-\sqrt{10}\right)}$$

Ikkunsidra li \left(2+\sqrt{10}\right)\left(2-\sqrt{10}\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}.

$$\frac{3\sqrt{10}\left(2-\sqrt{10}\right)}{2^{2}-\left(\sqrt{10}\right)^{2}}$$

Ikkwadra 2. Ikkwadra \sqrt{10}.

$$\frac{3\sqrt{10}\left(2-\sqrt{10}\right)}{4-10}$$

Naqqas 10 minn 4 biex tikseb -6.

$$\frac{3\sqrt{10}\left(2-\sqrt{10}\right)}{-6}$$

Uża l-propjetà distributtiva biex timmultiplika 3\sqrt{10} b'2-\sqrt{10}.

$$\frac{6\sqrt{10}-3\left(\sqrt{10}\right)^{2}}{-6}$$

Il-kwadrat ta' \sqrt{10} huwa 10.

$$\frac{6\sqrt{10}-3\times 10}{-6}$$

Immultiplika -3 u 10 biex tikseb -30.

$$\frac{6\sqrt{10}-30}{-6}$$

Iddividi kull terminu ta' 6\sqrt{10}-30 b'-6 biex tikseb-\sqrt{10}+5.

$$-\sqrt{10}+5$$