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

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

I-evaluate

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

Mga Hakbang ng Solution

Gamitin ang binomial theorem na \left(a-b\right)^{2}=a^{2}-2ab+b^{2} para palawakin ang \left(0.2\sqrt{2}-0.06\right)^{2}.

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

Ang square ng \sqrt{2} ay 2.

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

I-multiply ang 0.04 at 2 para makuha ang 0.08.

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

Idagdag ang 0.08 at 0.0036 para makuha ang 0.0836.

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

I-rationalize ang denominator ng \frac{2\left(0.8+\sqrt{2}\right)}{0.0836-0.024\sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa 0.0836+0.024\sqrt{2}.

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

Isaalang-alang ang \left(0.0836-0.024\sqrt{2}\right)\left(0.0836+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}.

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

Kalkulahin ang 0.0836 sa power ng 2 at kunin ang 0.00698896.

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

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

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

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

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

Ang square ng \sqrt{2} ay 2.

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

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

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

I-subtract ang 0.001152 mula sa 0.00698896 para makuha ang 0.00583696.

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

I-divide ang 2\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right) gamit ang 0.00583696 para makuha ang \frac{12500000}{36481}\left(0.8+\sqrt{2}\right)\left(0.0836+0.024\sqrt{2}\right).

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

Gamitin ang distributive property para i-multiply ang \frac{12500000}{36481} gamit ang 0.8+\sqrt{2}.

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

Gamitin ang distributive property para i-multiply ang \frac{10000000}{36481}+\frac{12500000}{36481}\sqrt{2} sa 0.0836+0.024\sqrt{2} at para pagsamahin ang magkakatulad na term.

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

Ang square ng \sqrt{2} ay 2.

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

I-multiply ang \frac{300000}{36481} at 2 para makuha ang \frac{600000}{36481}.

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

Idagdag ang \frac{836000}{36481} at \frac{600000}{36481} para makuha ang \frac{1436000}{36481}.

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