Resolver (2-sqrt{3})+(1/3)^-1-(3-7sqrt{2})^0-(-1)^2018+sqrt{4}+(1/4)^-2

$$( 2 - \sqrt { 3 } ) + ( \frac { 1 } { 3 } ) ^ { - 1 } - ( 3 - 7 \sqrt { 2 } ) ^ { 0 } - ( - 1 ) ^ { 2018 } + \sqrt { 4 } + ( \frac { 1 } { 4 } ) ^ { - 2 }$$

Avaliar

$$21-\sqrt{3}\approx 19,267949192$$

Passos Para a Resolução

Calcule \frac{1}{3} elevado a -1 e obtenha 3.

$$2-\sqrt{3}+3-\left(3-7\sqrt{2}\right)^{0}-\left(-1\right)^{2018}+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Some 2 e 3 para obter 5.

$$5-\sqrt{3}-\left(3-7\sqrt{2}\right)^{0}-\left(-1\right)^{2018}+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Calcule 3-7\sqrt{2} elevado a 0 e obtenha 1.

$$5-\sqrt{3}-1-\left(-1\right)^{2018}+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Subtraia 1 de 5 para obter 4.

$$4-\sqrt{3}-\left(-1\right)^{2018}+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Calcule -1 elevado a 2018 e obtenha 1.

$$4-\sqrt{3}-1+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Subtraia 1 de 4 para obter 3.

$$3-\sqrt{3}+\sqrt{4}+\left(\frac{1}{4}\right)^{-2}$$

Calcule a raiz quadrada de 4 e obtenha 2.

$$3-\sqrt{3}+2+\left(\frac{1}{4}\right)^{-2}$$

Some 3 e 2 para obter 5.

$$5-\sqrt{3}+\left(\frac{1}{4}\right)^{-2}$$

Calcule \frac{1}{4} elevado a -2 e obtenha 16.

$$5-\sqrt{3}+16$$

Some 5 e 16 para obter 21.

$$21-\sqrt{3}$$