Solve 5/6(sqrt{3+2)}

$$\frac { 5 } { 6 ( \sqrt { 3 } + 2 ) }$$

Evaluate

$$-\frac{5\sqrt{3}}{6}+\frac{5}{3}\approx 0.223290994$$

Solution Steps

Use the distributive property to multiply 6 by \sqrt{3}+2.

$$\frac{5}{6\sqrt{3}+12}$$

Rationalize the denominator of \frac{5}{6\sqrt{3}+12} by multiplying numerator and denominator by 6\sqrt{3}-12.

$$\frac{5\left(6\sqrt{3}-12\right)}{\left(6\sqrt{3}+12\right)\left(6\sqrt{3}-12\right)}$$

Consider \left(6\sqrt{3}+12\right)\left(6\sqrt{3}-12\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{5\left(6\sqrt{3}-12\right)}{\left(6\sqrt{3}\right)^{2}-12^{2}}$$

Expand \left(6\sqrt{3}\right)^{2}.

$$\frac{5\left(6\sqrt{3}-12\right)}{6^{2}\left(\sqrt{3}\right)^{2}-12^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{5\left(6\sqrt{3}-12\right)}{36\left(\sqrt{3}\right)^{2}-12^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{5\left(6\sqrt{3}-12\right)}{36\times 3-12^{2}}$$

Multiply 36 and 3 to get 108.

$$\frac{5\left(6\sqrt{3}-12\right)}{108-12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{5\left(6\sqrt{3}-12\right)}{108-144}$$

Subtract 144 from 108 to get -36.

$$\frac{5\left(6\sqrt{3}-12\right)}{-36}$$

Use the distributive property to multiply 5 by 6\sqrt{3}-12.

$$\frac{30\sqrt{3}-60}{-36}$$