Issolvi frac{sqrt{2}left(4-sqrt{2}right)}{2left(sqrt{2}+1right)}

$$\frac{ \sqrt{ 2 } \left( 4- \sqrt{ 2 } \right) }{ 2 \left( \sqrt{ 2 } +1 \right) }$$

Evalwa

$$5-3\sqrt{2}\approx 0.757359313$$

Passi tas-Soluzzjonijiet

Uża l-propjetà distributtiva biex timmultiplika \sqrt{2} b'4-\sqrt{2}.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{4\sqrt{2}-2}{2\left(\sqrt{2}+1\right)}$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'\sqrt{2}+1.

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

Irrazzjonalizza d-denominatur tal-\frac{4\sqrt{2}-2}{2\sqrt{2}+2} billi timmultiplika in-numeratur u d-denominatur mill-2\sqrt{2}-2.

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

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

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

Espandi \left(2\sqrt{2}\right)^{2}.

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

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

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

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{4\times 2-2^{2}}$$

Immultiplika 4 u 2 biex tikseb 8.

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{8-2^{2}}$$

Ikkalkula 2 bil-power ta' 2 u tikseb 4.

$$\frac{\left(4\sqrt{2}-2\right)\left(2\sqrt{2}-2\right)}{8-4}$$

Naqqas 4 minn 8 biex tikseb 4.

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

Applika l-propjetà distributtiva billi timmultiplika kull terminu ta' 4\sqrt{2}-2 b'kull terminu ta' 2\sqrt{2}-2.

$$\frac{8\left(\sqrt{2}\right)^{2}-8\sqrt{2}-4\sqrt{2}+4}{4}$$

Il-kwadrat ta' \sqrt{2} huwa 2.

$$\frac{8\times 2-8\sqrt{2}-4\sqrt{2}+4}{4}$$

Immultiplika 8 u 2 biex tikseb 16.

$$\frac{16-8\sqrt{2}-4\sqrt{2}+4}{4}$$

Ikkombina -8\sqrt{2} u -4\sqrt{2} biex tikseb -12\sqrt{2}.

$$\frac{16-12\sqrt{2}+4}{4}$$

Żid 16 u 4 biex tikseb 20.

$$\frac{20-12\sqrt{2}}{4}$$

Iddividi kull terminu ta' 20-12\sqrt{2} b'4 biex tikseb5-3\sqrt{2}.

$$5-3\sqrt{2}$$