Solve 10^{2}+sqrt{3^3*5}div2-4^2+3^2*3^2=

$$10 ^ { 2 } + \sqrt { 3 ^ { 3 } \times 5 } \div 2 - 4 ^ { 2 } + 3 ^ { 2 } \times 3 ^ { 2 } =$$

Evaluate

$$\frac{3\left(\sqrt{15}+110\right)}{2}\approx 170.809475019$$

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$10^{2}+\frac{\sqrt{3^{3}\times 5}}{2}-4^{2}+3^{4}$$

Calculate 10 to the power of 2 and get 100.

$$100+\frac{\sqrt{3^{3}\times 5}}{2}-4^{2}+3^{4}$$

Calculate 3 to the power of 3 and get 27.

$$100+\frac{\sqrt{27\times 5}}{2}-4^{2}+3^{4}$$

Multiply 27 and 5 to get 135.

$$100+\frac{\sqrt{135}}{2}-4^{2}+3^{4}$$

Factor 135=3^{2}\times 15. Rewrite the square root of the product \sqrt{3^{2}\times 15} as the product of square roots \sqrt{3^{2}}\sqrt{15}. Take the square root of 3^{2}.

$$100+\frac{3\sqrt{15}}{2}-4^{2}+3^{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 100 times \frac{2}{2}.

$$\frac{100\times 2}{2}+\frac{3\sqrt{15}}{2}-4^{2}+3^{4}$$

Since \frac{100\times 2}{2} and \frac{3\sqrt{15}}{2} have the same denominator, add them by adding their numerators.

$$\frac{100\times 2+3\sqrt{15}}{2}-4^{2}+3^{4}$$

Do the multiplications in 100\times 2+3\sqrt{15}.

$$\frac{200+3\sqrt{15}}{2}-4^{2}+3^{4}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{200+3\sqrt{15}}{2}-16+3^{4}$$

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

$$\frac{200+3\sqrt{15}}{2}-\frac{16\times 2}{2}+3^{4}$$

Since \frac{200+3\sqrt{15}}{2} and \frac{16\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{200+3\sqrt{15}-16\times 2}{2}+3^{4}$$

Do the multiplications in 200+3\sqrt{15}-16\times 2.

$$\frac{200+3\sqrt{15}-32}{2}+3^{4}$$

Do the calculations in 200+3\sqrt{15}-32.

$$\frac{168+3\sqrt{15}}{2}+3^{4}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{168+3\sqrt{15}}{2}+81$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81 times \frac{2}{2}.

$$\frac{168+3\sqrt{15}}{2}+\frac{81\times 2}{2}$$

Since \frac{168+3\sqrt{15}}{2} and \frac{81\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{168+3\sqrt{15}+81\times 2}{2}$$

Do the multiplications in 168+3\sqrt{15}+81\times 2.

$$\frac{168+3\sqrt{15}+162}{2}$$

Do the calculations in 168+3\sqrt{15}+162.

$$\frac{330+3\sqrt{15}}{2}$$

Factor

$$\frac{3 {(\sqrt{15} + 110)}}{2} = 170.80947501931112$$