Solve sqrt{4}-|-2|+(-1)^1000-sqrt{(-3)^2}+(sqrt{5})^2+(1/3)^-1-(sqrt{3}-1)

$$\sqrt { 4 } - | - 2 | + ( - 1 ) ^ { 1000 } - \sqrt { ( - 3 ) ^ { 2 } } + ( \sqrt { 5 } ) ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { - 1 } - ( \sqrt { 3 } - 1 )$$

Evaluate

$$7-\sqrt{3}\approx 5.267949192$$

Solution Steps

Calculate the square root of 4 and get 2.

$$2-|-2|+\left(-1\right)^{1000}-\sqrt{\left(-3\right)^{2}}+\left(\sqrt{5}\right)^{2}+\left(\frac{1}{3}\right)^{-1}-\left(\sqrt{3}-1\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -2 is 2.

$$2-2+\left(-1\right)^{1000}-\sqrt{\left(-3\right)^{2}}+\left(\sqrt{5}\right)^{2}+\left(\frac{1}{3}\right)^{-1}-\left(\sqrt{3}-1\right)$$

Subtract 2 from 2 to get 0.

$$0+\left(-1\right)^{1000}-\sqrt{\left(-3\right)^{2}}+\left(\sqrt{5}\right)^{2}+\left(\frac{1}{3}\right)^{-1}-\left(\sqrt{3}-1\right)$$

Calculate -1 to the power of 1000 and get 1.

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

Add 0 and 1 to get 1.

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

Calculate -3 to the power of 2 and get 9.

$$1-\sqrt{9}+\left(\sqrt{5}\right)^{2}+\left(\frac{1}{3}\right)^{-1}-\left(\sqrt{3}-1\right)$$

Calculate the square root of 9 and get 3.

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

Subtract 3 from 1 to get -2.

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

The square of \sqrt{5} is 5.

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

Add -2 and 5 to get 3.

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

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

$$3+3-\left(\sqrt{3}-1\right)$$

Add 3 and 3 to get 6.

$$6-\left(\sqrt{3}-1\right)$$

To find the opposite of \sqrt{3}-1, find the opposite of each term.

$$6-\sqrt{3}+1$$

Add 6 and 1 to get 7.

$$7-\sqrt{3}$$