Solve sqrt{(3*5-10:2)^{2}:5^{2}+(15+7*3)^3:(2*7+2^2)^3}+2^2

$$\sqrt { ( 3 \times 5 - 10 : 2 ) ^ { 2 } : 5 ^ { 2 } + ( 15 + 7 \times 3 ) ^ { 3 } : ( 2 \times 7 + 2 ^ { 2 } ) ^ { 3 } } + 2 ^ { 2 }$$

Evaluate

$$2\left(\sqrt{3}+2\right)\approx 7.464101615$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\sqrt{\frac{\left(15-\frac{10}{2}\right)^{2}}{5^{2}}+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Divide 10 by 2 to get 5.

$$\sqrt{\frac{\left(15-5\right)^{2}}{5^{2}}+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Subtract 5 from 15 to get 10.

$$\sqrt{\frac{10^{2}}{5^{2}}+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Calculate 10 to the power of 2 and get 100.

$$\sqrt{\frac{100}{5^{2}}+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{\frac{100}{25}+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Divide 100 by 25 to get 4.

$$\sqrt{4+\frac{\left(15+7\times 3\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Multiply 7 and 3 to get 21.

$$\sqrt{4+\frac{\left(15+21\right)^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Add 15 and 21 to get 36.

$$\sqrt{4+\frac{36^{3}}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Calculate 36 to the power of 3 and get 46656.

$$\sqrt{4+\frac{46656}{\left(2\times 7+2^{2}\right)^{3}}}+2^{2}$$

Multiply 2 and 7 to get 14.

$$\sqrt{4+\frac{46656}{\left(14+2^{2}\right)^{3}}}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\sqrt{4+\frac{46656}{\left(14+4\right)^{3}}}+2^{2}$$

Add 14 and 4 to get 18.

$$\sqrt{4+\frac{46656}{18^{3}}}+2^{2}$$

Calculate 18 to the power of 3 and get 5832.

$$\sqrt{4+\frac{46656}{5832}}+2^{2}$$

Divide 46656 by 5832 to get 8.

$$\sqrt{4+8}+2^{2}$$

Add 4 and 8 to get 12.

$$\sqrt{12}+2^{2}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$2\sqrt{3}+2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$2\sqrt{3}+4$$