Solve sqrt{(3/7+5/2)^2:(1+13/28)^2-3/8*2^2+frac{45}{2}}=

$$\sqrt { ( \frac { 3 } { 7 } + \frac { 5 } { 2 } ) ^ { 2 } : ( 1 + \frac { 13 } { 28 } ) ^ { 2 } - \frac { 3 } { 8 } \cdot 2 ^ { 2 } + \frac { 45 } { 2 } } =$$

Evaluate

$$5$$

Solution Steps

Add \frac{3}{7} and \frac{5}{2} to get \frac{41}{14}.

$$\sqrt{\frac{\left(\frac{41}{14}\right)^{2}}{\left(1+\frac{13}{28}\right)^{2}}-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Calculate \frac{41}{14} to the power of 2 and get \frac{1681}{196}.

$$\sqrt{\frac{\frac{1681}{196}}{\left(1+\frac{13}{28}\right)^{2}}-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Add 1 and \frac{13}{28} to get \frac{41}{28}.

$$\sqrt{\frac{\frac{1681}{196}}{\left(\frac{41}{28}\right)^{2}}-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Calculate \frac{41}{28} to the power of 2 and get \frac{1681}{784}.

$$\sqrt{\frac{\frac{1681}{196}}{\frac{1681}{784}}-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Divide \frac{1681}{196} by \frac{1681}{784} by multiplying \frac{1681}{196} by the reciprocal of \frac{1681}{784}.

$$\sqrt{\frac{1681}{196}\times \frac{784}{1681}-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Multiply \frac{1681}{196} and \frac{784}{1681} to get 4.

$$\sqrt{4-\frac{3}{8}\times 2^{2}+\frac{45}{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4-\frac{3}{8}\times 4+\frac{45}{2}}$$

Multiply \frac{3}{8} and 4 to get \frac{3}{2}.

$$\sqrt{4-\frac{3}{2}+\frac{45}{2}}$$

Subtract \frac{3}{2} from 4 to get \frac{5}{2}.

$$\sqrt{\frac{5}{2}+\frac{45}{2}}$$

Add \frac{5}{2} and \frac{45}{2} to get 25.

$$\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$5$$

Factor

$$5$$