Solve sqrt{3*2^{3}+30*2-3^{2}-3^12:3^10+5^3:5^2*5+6}=

$$\sqrt { 3 \cdot 2 ^ { 3 } + 30 \cdot 2 - 3 ^ { 2 } - 3 ^ { 12 } : 3 ^ { 10 } + 5 ^ { 3 } : 5 ^ { 2 } \cdot 5 + 6 } =$$

Evaluate

$$\sqrt{97}\approx 9.848857802$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 10 from 12 to get 2.

$$\sqrt{3\times 2^{3}+30\times 2-3^{2}-3^{2}+\frac{5^{3}}{5^{2}}\times 5+6}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 3 to get 1.

$$\sqrt{3\times 2^{3}+30\times 2-3^{2}-3^{2}+5^{1}\times 5+6}$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$\sqrt{3\times 2^{3}+30\times 2-3^{2}-3^{2}+5^{2}+6}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{3\times 8+30\times 2-3^{2}-3^{2}+5^{2}+6}$$

Multiply 3 and 8 to get 24.

$$\sqrt{24+30\times 2-3^{2}-3^{2}+5^{2}+6}$$

Multiply 30 and 2 to get 60.

$$\sqrt{24+60-3^{2}-3^{2}+5^{2}+6}$$

Add 24 and 60 to get 84.

$$\sqrt{84-3^{2}-3^{2}+5^{2}+6}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{84-9-3^{2}+5^{2}+6}$$

Subtract 9 from 84 to get 75.

$$\sqrt{75-3^{2}+5^{2}+6}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{75-9+5^{2}+6}$$

Subtract 9 from 75 to get 66.

$$\sqrt{66+5^{2}+6}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{66+25+6}$$

Add 66 and 25 to get 91.

$$\sqrt{91+6}$$

Add 91 and 6 to get 97.

$$\sqrt{97}$$