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

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

Evaluate

$$21-\sqrt{3}\approx 19.267949192$$

Solution Steps

Calculate \frac{1}{3} to the power of -1 and get 3.

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

Add 2 and 3 to get 5.

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

Calculate 3-7\sqrt{2} to the power of 0 and get 1.

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

Subtract 1 from 5 to get 4.

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

Calculate -1 to the power of 2018 and get 1.

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

Subtract 1 from 4 to get 3.

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

Calculate the square root of 4 and get 2.

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

Add 3 and 2 to get 5.

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

Calculate \frac{1}{4} to the power of -2 and get 16.

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

Add 5 and 16 to get 21.

$$21-\sqrt{3}$$