Solve (sqrt{3}-2)(sqrt{3}+2)-|sqrt[3]{-27}-pi^0|-(-1/3)

$$( \sqrt { 3 } - 2 ) ( \sqrt { 3 } + 2 ) - | \sqrt[ 3 ] { - 27 } - \pi ^ { 0 } | - ( - \frac { 1 } { 3 } )$$

Evaluate

$$-\frac{14}{3}\approx -4.666666667$$

Solution Steps

Consider \left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 2.

$$\left(\sqrt{3}\right)^{2}-4-|\sqrt[3]{-27}-\pi ^{0}|-\left(-\frac{1}{3}\right)$$

The square of \sqrt{3} is 3.

$$3-4-|\sqrt[3]{-27}-\pi ^{0}|-\left(-\frac{1}{3}\right)$$

Subtract 4 from 3 to get -1.

$$-1-|\sqrt[3]{-27}-\pi ^{0}|-\left(-\frac{1}{3}\right)$$

Calculate \sqrt[3]{-27} and get -3.

$$-1-|-3-\pi ^{0}|-\left(-\frac{1}{3}\right)$$

Calculate \pi to the power of 0 and get 1.

$$-1-|-3-1|-\left(-\frac{1}{3}\right)$$

Subtract 1 from -3 to get -4.

$$-1-|-4|-\left(-\frac{1}{3}\right)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$-1-4-\left(-\frac{1}{3}\right)$$

Subtract 4 from -1 to get -5.

$$-5-\left(-\frac{1}{3}\right)$$

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$-5+\frac{1}{3}$$

Add -5 and \frac{1}{3} to get -\frac{14}{3}.

$$-\frac{14}{3}$$

Factor

$$-\frac{14}{3} = -4\frac{2}{3} = -4.666666666666667$$