Solve 2sqrt{144/87}+7^7*sqrt[3]{8}

$$2 \sqrt { \frac { 144 } { 87 } } + 7 ^ { 7 } \cdot \sqrt[ 3 ] { 8 }$$

Evaluate

$$\frac{8\sqrt{87}}{29}+1647086\approx 1647088.573070084$$

Short Solution Steps

Reduce the fraction \frac{144}{87} to lowest terms by extracting and canceling out 3.

$$2\sqrt{\frac{48}{29}}+7^{7}\sqrt[3]{8}$$

Rewrite the square root of the division \sqrt{\frac{48}{29}} as the division of square roots \frac{\sqrt{48}}{\sqrt{29}}.

$$2\times \frac{\sqrt{48}}{\sqrt{29}}+7^{7}\sqrt[3]{8}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$2\times \frac{4\sqrt{3}}{\sqrt{29}}+7^{7}\sqrt[3]{8}$$

Rationalize the denominator of \frac{4\sqrt{3}}{\sqrt{29}} by multiplying numerator and denominator by \sqrt{29}.

$$2\times \frac{4\sqrt{3}\sqrt{29}}{\left(\sqrt{29}\right)^{2}}+7^{7}\sqrt[3]{8}$$

The square of \sqrt{29} is 29.

$$2\times \frac{4\sqrt{3}\sqrt{29}}{29}+7^{7}\sqrt[3]{8}$$

To multiply \sqrt{3} and \sqrt{29}, multiply the numbers under the square root.

$$2\times \frac{4\sqrt{87}}{29}+7^{7}\sqrt[3]{8}$$

Express 2\times \frac{4\sqrt{87}}{29} as a single fraction.

$$\frac{2\times 4\sqrt{87}}{29}+7^{7}\sqrt[3]{8}$$

Calculate 7 to the power of 7 and get 823543.

$$\frac{2\times 4\sqrt{87}}{29}+823543\sqrt[3]{8}$$

Calculate \sqrt[3]{8} and get 2.

$$\frac{2\times 4\sqrt{87}}{29}+823543\times 2$$

Multiply 823543 and 2 to get 1647086.

$$\frac{2\times 4\sqrt{87}}{29}+1647086$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1647086 times \frac{29}{29}.

$$\frac{2\times 4\sqrt{87}}{29}+\frac{1647086\times 29}{29}$$

Since \frac{2\times 4\sqrt{87}}{29} and \frac{1647086\times 29}{29} have the same denominator, add them by adding their numerators.

$$\frac{2\times 4\sqrt{87}+1647086\times 29}{29}$$

Do the multiplications in 2\times 4\sqrt{87}+1647086\times 29.

$$\frac{8\sqrt{87}[phone]}{29}$$