Solve 2*sqrt[3]{343}+3*sqrt[3]{729}-5*sqrt{216}+(sqrt{7}+sqrt[4]{81}*4+sqrt{4})

$$2 \times \sqrt[ 3 ] { 343 } + 3 \times \sqrt[ 3 ] { 729 } - 5 \times \sqrt { 216 } + ( \sqrt { 7 } + \sqrt[ 4 ] { 81 } \times 4 + \sqrt { 4 } )$$

Evaluate

$$\sqrt{7}+55-30\sqrt{6}\approx -15.838940972$$

Solution Steps

Calculate \sqrt[3]{343} and get 7.

$$2\times 7+3\sqrt[3]{729}-5\sqrt{216}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Multiply 2 and 7 to get 14.

$$14+3\sqrt[3]{729}-5\sqrt{216}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Calculate \sqrt[3]{729} and get 9.

$$14+3\times 9-5\sqrt{216}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Multiply 3 and 9 to get 27.

$$14+27-5\sqrt{216}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Add 14 and 27 to get 41.

$$41-5\sqrt{216}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$41-5\times 6\sqrt{6}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Multiply -5 and 6 to get -30.

$$41-30\sqrt{6}+\sqrt{7}+\sqrt[4]{81}\times 4+\sqrt{4}$$

Calculate \sqrt[4]{81} and get 3.

$$41-30\sqrt{6}+\sqrt{7}+3\times 4+\sqrt{4}$$

Multiply 3 and 4 to get 12.

$$41-30\sqrt{6}+\sqrt{7}+12+\sqrt{4}$$

Add 41 and 12 to get 53.

$$53-30\sqrt{6}+\sqrt{7}+\sqrt{4}$$

Calculate the square root of 4 and get 2.

$$53-30\sqrt{6}+\sqrt{7}+2$$

Add 53 and 2 to get 55.

$$55-30\sqrt{6}+\sqrt{7}$$