Solve (frac{5sqrt{10}}{4}+1)^2+3^2

$$( \frac { 5 \sqrt { 10 } } { 4 } + 1 ) ^ { 2 } + 3 ^ { 2 }$$

Evaluate

$$\frac{5\sqrt{10}}{2}+\frac{205}{8}\approx 33.53069415$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\left(\frac{5\sqrt{10}}{4}+\frac{4}{4}\right)^{2}+3^{2}$$

Since \frac{5\sqrt{10}}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\left(\frac{5\sqrt{10}+4}{4}\right)^{2}+3^{2}$$

To raise \frac{5\sqrt{10}+4}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{4^{2}}{4^{2}}.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+\frac{9\times 4^{2}}{4^{2}}$$

Since \frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}} and \frac{9\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5\sqrt{10}+4\right)^{2}+9\times 4^{2}}{4^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5\sqrt{10}+4\right)^{2}.

$$\frac{25\left(\sqrt{10}\right)^{2}+40\sqrt{10}+16}{4^{2}}+9$$

The square of \sqrt{10} is 10.

$$\frac{25\times 10+40\sqrt{10}+16}{4^{2}}+9$$

Multiply 25 and 10 to get 250.

$$\frac{250+40\sqrt{10}+16}{4^{2}}+9$$

Add 250 and 16 to get 266.

$$\frac{266+40\sqrt{10}}{4^{2}}+9$$

Calculate 4 to the power of 2 and get 16.

$$\frac{266+40\sqrt{10}}{16}+9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{16}{16}.

$$\frac{266+40\sqrt{10}}{16}+\frac{9\times 16}{16}$$

Since \frac{266+40\sqrt{10}}{16} and \frac{9\times 16}{16} have the same denominator, add them by adding their numerators.

$$\frac{266+40\sqrt{10}+9\times 16}{16}$$

Do the multiplications in 266+40\sqrt{10}+9\times 16.

$$\frac{266+40\sqrt{10}+144}{16}$$

Do the calculations in 266+40\sqrt{10}+144.

$$\frac{410+40\sqrt{10}}{16}$$

Expand

$$\frac{5 \sqrt{10}}{2} + \frac{205}{8} = 33.53069415$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{4}{4}.

$$\left(\frac{5\sqrt{10}}{4}+\frac{4}{4}\right)^{2}+3^{2}$$

Since \frac{5\sqrt{10}}{4} and \frac{4}{4} have the same denominator, add them by adding their numerators.

$$\left(\frac{5\sqrt{10}+4}{4}\right)^{2}+3^{2}$$

To raise \frac{5\sqrt{10}+4}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{4^{2}}{4^{2}}.

$$\frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}}+\frac{9\times 4^{2}}{4^{2}}$$

Since \frac{\left(5\sqrt{10}+4\right)^{2}}{4^{2}} and \frac{9\times 4^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(5\sqrt{10}+4\right)^{2}+9\times 4^{2}}{4^{2}}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(5\sqrt{10}+4\right)^{2}.

$$\frac{25\left(\sqrt{10}\right)^{2}+40\sqrt{10}+16}{4^{2}}+9$$

The square of \sqrt{10} is 10.

$$\frac{25\times 10+40\sqrt{10}+16}{4^{2}}+9$$

Multiply 25 and 10 to get 250.

$$\frac{250+40\sqrt{10}+16}{4^{2}}+9$$

Add 250 and 16 to get 266.

$$\frac{266+40\sqrt{10}}{4^{2}}+9$$

Calculate 4 to the power of 2 and get 16.

$$\frac{266+40\sqrt{10}}{16}+9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{16}{16}.

$$\frac{266+40\sqrt{10}}{16}+\frac{9\times 16}{16}$$

Since \frac{266+40\sqrt{10}}{16} and \frac{9\times 16}{16} have the same denominator, add them by adding their numerators.

$$\frac{266+40\sqrt{10}+9\times 16}{16}$$

Do the multiplications in 266+40\sqrt{10}+9\times 16.

$$\frac{266+40\sqrt{10}+144}{16}$$

Do the calculations in 266+40\sqrt{10}+144.

$$\frac{410+40\sqrt{10}}{16}$$