Solve (frac{16+6sqrt{2}}{5})^2

$$( \frac { 16 + 6 \sqrt { 2 } } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{192\sqrt{2}+328}{25}\approx 23.981160159$$

Solution Steps

To raise \frac{16+6\sqrt{2}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(16+6\sqrt{2}\right)^{2}}{5^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(16+6\sqrt{2}\right)^{2}.

$$\frac{256+192\sqrt{2}+36\left(\sqrt{2}\right)^{2}}{5^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{256+192\sqrt{2}+36\times 2}{5^{2}}$$

Multiply 36 and 2 to get 72.

$$\frac{256+192\sqrt{2}+72}{5^{2}}$$

Add 256 and 72 to get 328.

$$\frac{328+192\sqrt{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{328+192\sqrt{2}}{25}$$

Expand

$$\frac{192 \sqrt{2} + 328}{25} = 23.98116015902537$$

Solution Steps

To raise \frac{16+6\sqrt{2}}{5} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(16+6\sqrt{2}\right)^{2}}{5^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(16+6\sqrt{2}\right)^{2}.

$$\frac{256+192\sqrt{2}+36\left(\sqrt{2}\right)^{2}}{5^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{256+192\sqrt{2}+36\times 2}{5^{2}}$$

Multiply 36 and 2 to get 72.

$$\frac{256+192\sqrt{2}+72}{5^{2}}$$

Add 256 and 72 to get 328.

$$\frac{328+192\sqrt{2}}{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{328+192\sqrt{2}}{25}$$