Solve (frac{sqrt{89}}{4})^2-(121/16)^2

$$( \frac { \sqrt { 89 } } { 4 } ) ^ { 2 } - ( 1 \frac { 21 } { 16 } ) ^ { 2 }$$

Evaluate

$$\frac{55}{256}=0.21484375$$

Solution Steps

To raise \frac{\sqrt{89}}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{89}\right)^{2}}{4^{2}}-\left(\frac{1\times 16+21}{16}\right)^{2}$$

Multiply 1 and 16 to get 16.

$$\frac{\left(\sqrt{89}\right)^{2}}{4^{2}}-\left(\frac{16+21}{16}\right)^{2}$$

Add 16 and 21 to get 37.

$$\frac{\left(\sqrt{89}\right)^{2}}{4^{2}}-\left(\frac{37}{16}\right)^{2}$$

Calculate \frac{37}{16} to the power of 2 and get \frac{1369}{256}.

$$\frac{\left(\sqrt{89}\right)^{2}}{4^{2}}-\frac{1369}{256}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4^{2} and 256 is 256. Multiply \frac{\left(\sqrt{89}\right)^{2}}{4^{2}} times \frac{16}{16}.

$$\frac{16\left(\sqrt{89}\right)^{2}}{256}-\frac{1369}{256}$$

Since \frac{16\left(\sqrt{89}\right)^{2}}{256} and \frac{1369}{256} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16\left(\sqrt{89}\right)^{2}-1369}{256}$$

The square of \sqrt{89} is 89.

$$\frac{89}{4^{2}}-\frac{1369}{256}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{89}{16}-\frac{1369}{256}$$

Subtract \frac{1369}{256} from \frac{89}{16} to get \frac{55}{256}.

$$\frac{55}{256}$$

Factor

$$\frac{5 \cdot 11}{2 ^ {8}} = 0.21484375$$