Issolvi frac{2left(0.8+sqrt{2}right)}{{left(0.2sqrt{2}-0.06right)}^2}

$$\frac{ 2 \left( 0.8+ \sqrt{ 2 } \right) }{ { \left(0.2 \sqrt{ 2 } -0.06 \right) }^{ 2 } }$$

Evalwa

$$\frac{1285000\sqrt{2}+1436000}{36481}\approx 89.176953144$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(0.2\sqrt{2}-0.06\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\left(\sqrt{2}\right)^{2}-0.024\sqrt{2}+0.0036}$$

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

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.04\times 2-0.024\sqrt{2}+0.0036}$$

Immultiplika 0.04 u 2 biex tikseb 0.08.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.08-0.024\sqrt{2}+0.0036}$$

Żid 0.08 u 0.0036 biex tikseb 0.0836.

$$\frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}}$$

Irrazzjonalizza d-denominatur tal-\frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}} billi timmultiplika in-numeratur u d-denominatur mill-0.0836+0.024\sqrt{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{\left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}$$

Ikkunsidra li \left(0.0836-0.024\sqrt{2}\right)\left(0.0836+0.024\sqrt{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}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.0836^{2}-\left(-0.024\sqrt{2}\right)^{2}}$$

Ikkalkula 0.0836 bil-power ta' 2 u tikseb 0.00698896.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\sqrt{2}\right)^{2}}$$

Espandi \left(-0.024\sqrt{2}\right)^{2}.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-\left(-0.024\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Ikkalkula -0.024 bil-power ta' 2 u tikseb 0.000576.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\left(\sqrt{2}\right)^{2}}$$

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

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.000576\times 2}$$

Immultiplika 0.000576 u 2 biex tikseb 0.001152.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00698896-0.001152}$$

Naqqas 0.001152 minn 0.00698896 biex tikseb 0.00583696.

$$\frac{2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)}{0.00583696}$$

Iddividi 2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right) b'0.00583696 biex tikseb\frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right).

$$\frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{12500000}{36481} b'0.8+\sqrt{2}.

$$\left(\frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2} b'0.0836+0.024\sqrt{2} u kkombina termini simili.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\left(\sqrt{2}\right)^{2}$$

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

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{300000}{36481}\times 2$$

Immultiplika \frac{300000}{36481} u 2 biex tikseb \frac{600000}{36481}.

$$\frac{836000}{36481}+\frac{1285000}{36481}\sqrt{2}+\frac{600000}{36481}$$

Żid \frac{836000}{36481} u \frac{600000}{36481} biex tikseb \frac{1436000}{36481}.

$$\frac{1436000}{36481}+\frac{1285000}{36481}\sqrt{2}$$