Solve (frac{5sqrt{330}}{12}-7)^2+4^2

$$( \frac { 5 \sqrt { 330 } } { 12 } - 7 ) ^ { 2 } + 4 ^ { 2 }$$

Evaluate

$$-\frac{35\sqrt{330}}{6}+\frac{2935}{24}\approx 16.323904273$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{12}{12}.

$$\left(\frac{5\sqrt{330}}{12}-\frac{7\times 12}{12}\right)^{2}+4^{2}$$

Since \frac{5\sqrt{330}}{12} and \frac{7\times 12}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{5\sqrt{330}-7\times 12}{12}\right)^{2}+4^{2}$$

Do the multiplications in 5\sqrt{330}-7\times 12.

$$\left(\frac{5\sqrt{330}-84}{12}\right)^{2}+4^{2}$$

To raise \frac{5\sqrt{330}-84}{12} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{12^{2}}{12^{2}}.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+\frac{16\times 12^{2}}{12^{2}}$$

Since \frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}} and \frac{16\times 12^{2}}{12^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5\sqrt{330}-84\right)^{2}+16\times 12^{2}}{12^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{330}-84\right)^{2}.

$$\frac{25\left(\sqrt{330}\right)^{2}-840\sqrt{330}+7056}{12^{2}}+16$$

The square of \sqrt{330} is 330.

$$\frac{25\times 330-840\sqrt{330}+7056}{12^{2}}+16$$

Multiply 25 and 330 to get 8250.

$$\frac{8250-840\sqrt{330}+7056}{12^{2}}+16$$

Add 8250 and 7056 to get 15306.

$$\frac{15306-840\sqrt{330}}{12^{2}}+16$$

Calculate 12 to the power of 2 and get 144.

$$\frac{15306-840\sqrt{330}}{144}+16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{144}{144}.

$$\frac{15306-840\sqrt{330}}{144}+\frac{16\times 144}{144}$$

Since \frac{15306-840\sqrt{330}}{144} and \frac{16\times 144}{144} have the same denominator, add them by adding their numerators.

$$\frac{15306-840\sqrt{330}+16\times 144}{144}$$

Do the multiplications in 15306-840\sqrt{330}+16\times 144.

$$\frac{15306-840\sqrt{330}+2304}{144}$$

Do the calculations in 15306-840\sqrt{330}+2304.

$$\frac{17610-840\sqrt{330}}{144}$$

Expand

$$-\frac{35 \sqrt{330}}{6} + \frac{2935}{24} = 16.323904273$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{12}{12}.

$$\left(\frac{5\sqrt{330}}{12}-\frac{7\times 12}{12}\right)^{2}+4^{2}$$

Since \frac{5\sqrt{330}}{12} and \frac{7\times 12}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{5\sqrt{330}-7\times 12}{12}\right)^{2}+4^{2}$$

Do the multiplications in 5\sqrt{330}-7\times 12.

$$\left(\frac{5\sqrt{330}-84}{12}\right)^{2}+4^{2}$$

To raise \frac{5\sqrt{330}-84}{12} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{12^{2}}{12^{2}}.

$$\frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}}+\frac{16\times 12^{2}}{12^{2}}$$

Since \frac{\left(5\sqrt{330}-84\right)^{2}}{12^{2}} and \frac{16\times 12^{2}}{12^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5\sqrt{330}-84\right)^{2}+16\times 12^{2}}{12^{2}}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5\sqrt{330}-84\right)^{2}.

$$\frac{25\left(\sqrt{330}\right)^{2}-840\sqrt{330}+7056}{12^{2}}+16$$

The square of \sqrt{330} is 330.

$$\frac{25\times 330-840\sqrt{330}+7056}{12^{2}}+16$$

Multiply 25 and 330 to get 8250.

$$\frac{8250-840\sqrt{330}+7056}{12^{2}}+16$$

Add 8250 and 7056 to get 15306.

$$\frac{15306-840\sqrt{330}}{12^{2}}+16$$

Calculate 12 to the power of 2 and get 144.

$$\frac{15306-840\sqrt{330}}{144}+16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{144}{144}.

$$\frac{15306-840\sqrt{330}}{144}+\frac{16\times 144}{144}$$

Since \frac{15306-840\sqrt{330}}{144} and \frac{16\times 144}{144} have the same denominator, add them by adding their numerators.

$$\frac{15306-840\sqrt{330}+16\times 144}{144}$$

Do the multiplications in 15306-840\sqrt{330}+16\times 144.

$$\frac{15306-840\sqrt{330}+2304}{144}$$

Do the calculations in 15306-840\sqrt{330}+2304.

$$\frac{17610-840\sqrt{330}}{144}$$