Solve frac{7sqrt{27}}{7}*7^7/35+2*6^3/7^2=

$$\frac { 7 \sqrt { 27 } } { 7 } \times \frac { 7 ^ { 7 } } { 35 } + \frac { 2 \times 6 ^ { 3 } } { 7 ^ { 2 } } =$$

Evaluate

$$\frac{352947\sqrt{3}}{5}+\frac{432}{49}\approx 122273.243602333$$

Solution Steps

Cancel out 7 and 7.

$$\sqrt{27}\times \frac{7^{7}}{35}+\frac{2\times 6^{3}}{7^{2}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\sqrt{3}\times \frac{7^{7}}{35}+\frac{2\times 6^{3}}{7^{2}}$$

Calculate 7 to the power of 7 and get 823543.

$$3\sqrt{3}\times \frac{823543}{35}+\frac{2\times 6^{3}}{7^{2}}$$

Reduce the fraction \frac{823543}{35} to lowest terms by extracting and canceling out 7.

$$3\sqrt{3}\times \frac{117649}{5}+\frac{2\times 6^{3}}{7^{2}}$$

Express 3\times \frac{117649}{5} as a single fraction.

$$\frac{3\times 117649}{5}\sqrt{3}+\frac{2\times 6^{3}}{7^{2}}$$

Multiply 3 and 117649 to get 352947.

$$\frac{352947}{5}\sqrt{3}+\frac{2\times 6^{3}}{7^{2}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{352947}{5}\sqrt{3}+\frac{2\times 216}{7^{2}}$$

Multiply 2 and 216 to get 432.

$$\frac{352947}{5}\sqrt{3}+\frac{432}{7^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{352947}{5}\sqrt{3}+\frac{432}{49}$$

Factor

$$\frac{3 {(5764801 \sqrt{3} + 720)}}{245} = 122273.24360233311$$