Solve sqrt{15/4}+22/3*(11/2)^2-3div11/5=

$$\sqrt { 1 \frac { 5 } { 4 } } + 2 \frac { 2 } { 3 } \cdot ( 1 \frac { 1 } { 2 } ) ^ { 2 } - 3 \div 1 \frac { 1 } { 5 } =$$

Evaluate

$$5$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 5 to get 9.

$$\sqrt{\frac{9}{4}}+\frac{2\times 3+2}{3}\times \left(\frac{1\times 2+1}{2}\right)^{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Multiply 2 and 3 to get 6.

$$\frac{3}{2}+\frac{6+2}{3}\times \left(\frac{1\times 2+1}{2}\right)^{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Add 6 and 2 to get 8.

$$\frac{3}{2}+\frac{8}{3}\times \left(\frac{1\times 2+1}{2}\right)^{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Multiply 1 and 2 to get 2.

$$\frac{3}{2}+\frac{8}{3}\times \left(\frac{2+1}{2}\right)^{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}+\frac{8}{3}\times \left(\frac{3}{2}\right)^{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{3}{2}+\frac{8}{3}\times \frac{9}{4}-\frac{3}{\frac{1\times 5+1}{5}}$$

Multiply \frac{8}{3} and \frac{9}{4} to get 6.

$$\frac{3}{2}+6-\frac{3}{\frac{1\times 5+1}{5}}$$

Add \frac{3}{2} and 6 to get \frac{15}{2}.

$$\frac{15}{2}-\frac{3}{\frac{1\times 5+1}{5}}$$

Divide 3 by \frac{1\times 5+1}{5} by multiplying 3 by the reciprocal of \frac{1\times 5+1}{5}.

$$\frac{15}{2}-\frac{3\times 5}{1\times 5+1}$$

Multiply 3 and 5 to get 15.

$$\frac{15}{2}-\frac{15}{1\times 5+1}$$

Multiply 1 and 5 to get 5.

$$\frac{15}{2}-\frac{15}{5+1}$$

Add 5 and 1 to get 6.

$$\frac{15}{2}-\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{15}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from \frac{15}{2} to get 5.

$$5$$

Factor

$$5$$