Lutasin ang frac{1.6+2sqrt{2}}{0.083-0.024sqrt{2}}

$$\frac{ 1.6+2 \sqrt{ 2 } }{ 0.083-0.024 \sqrt{ 2 } }$$

I-evaluate

$$\frac{204400\sqrt{2}+228800}{5737}\approx 90.267605395$$

Mga Hakbang ng Solution

I-rationalize ang denominator ng \frac{1.6+2\sqrt{2}}{0.083-0.024\sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa 0.083+0.024\sqrt{2}.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{\left(0.083-0.024\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}$$

Isaalang-alang ang \left(0.083-0.024\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right). Maaaring ma-transform ang pag-multiply sa difference ng mga square gamit ang rule na: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.083^{2}-\left(-0.024\sqrt{2}\right)^{2}}$$

Kalkulahin ang 0.083 sa power ng 2 at kunin ang 0.006889.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-\left(-0.024\sqrt{2}\right)^{2}}$$

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

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-\left(-0.024\right)^{2}\left(\sqrt{2}\right)^{2}}$$

Kalkulahin ang -0.024 sa power ng 2 at kunin ang 0.000576.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.000576\left(\sqrt{2}\right)^{2}}$$

Ang square ng \sqrt{2} ay 2.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.000576\times 2}$$

I-multiply ang 0.000576 at 2 para makuha ang 0.001152.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.006889-0.001152}$$

I-subtract ang 0.001152 mula sa 0.006889 para makuha ang 0.005737.

$$\frac{\left(1.6+2\sqrt{2}\right)\left(0.083+0.024\sqrt{2}\right)}{0.005737}$$

Ilapat ang distributive property sa pamamagitan ng pag-multiply sa bawat term ng 1.6+2\sqrt{2} sa bawat term ng 0.083+0.024\sqrt{2}.

$$\frac{0.1328+0.0384\sqrt{2}+0.166\sqrt{2}+0.048\left(\sqrt{2}\right)^{2}}{0.005737}$$

Pagsamahin ang 0.0384\sqrt{2} at 0.166\sqrt{2} para makuha ang 0.2044\sqrt{2}.

$$\frac{0.1328+0.2044\sqrt{2}+0.048\left(\sqrt{2}\right)^{2}}{0.005737}$$

Ang square ng \sqrt{2} ay 2.

$$\frac{0.1328+0.2044\sqrt{2}+0.048\times 2}{0.005737}$$

I-multiply ang 0.048 at 2 para makuha ang 0.096.

$$\frac{0.1328+0.2044\sqrt{2}+0.096}{0.005737}$$

Idagdag ang 0.1328 at 0.096 para makuha ang 0.2288.

$$\frac{0.2288+0.2044\sqrt{2}}{0.005737}$$