Solve {sqrt{400}-[(10^2div5)-3(5^3-20)]-45}

$$\{ \sqrt { 400 } - [ ( 10 ^ { 2 } \div 5 ) - 3 ( 5 ^ { 3 } - 20 ) ] - 45 \}$$

Evaluate

$$270$$

Solution Steps

Calculate the square root of 400 and get 20.

$$20-\left(\frac{10^{2}}{5}-3\left(5^{3}-20\right)\right)-45$$

Calculate 10 to the power of 2 and get 100.

$$20-\left(\frac{100}{5}-3\left(5^{3}-20\right)\right)-45$$

Divide 100 by 5 to get 20.

$$20-\left(20-3\left(5^{3}-20\right)\right)-45$$

Calculate 5 to the power of 3 and get 125.

$$20-\left(20-3\left(125-20\right)\right)-45$$

Subtract 20 from 125 to get 105.

$$20-\left(20-3\times 105\right)-45$$

Multiply 3 and 105 to get 315.

$$20-\left(20-315\right)-45$$

Subtract 315 from 20 to get -295.

$$20-\left(-295\right)-45$$

The opposite of -295 is 295.

$$20+295-45$$

Add 20 and 295 to get 315.

$$315-45$$

Subtract 45 from 315 to get 270.

$$270$$

Factor

$$2\times 3^{3}\times 5$$