Solve (5*5/2)*(7*(5sqrt{2})-2)

$$( \frac { 5 \times 5 } { 2 } ) \cdot ( 7 \times ( 5 \sqrt { 2 } ) - 2 )$$

Evaluate

$$\frac{875\sqrt{2}}{2}-25\approx 593.718433538$$

Solution Steps

Multiply 5 and 5 to get 25.

$$\frac{25}{2}\left(7\times 5\sqrt{2}-2\right)$$

Multiply 7 and 5 to get 35.

$$\frac{25}{2}\left(35\sqrt{2}-2\right)$$

Use the distributive property to multiply \frac{25}{2} by 35\sqrt{2}-2.

$$\frac{25}{2}\times 35\sqrt{2}+\frac{25}{2}\left(-2\right)$$

Express \frac{25}{2}\times 35 as a single fraction.

$$\frac{25\times 35}{2}\sqrt{2}+\frac{25}{2}\left(-2\right)$$

Multiply 25 and 35 to get 875.

$$\frac{875}{2}\sqrt{2}+\frac{25}{2}\left(-2\right)$$

Express \frac{25}{2}\left(-2\right) as a single fraction.

$$\frac{875}{2}\sqrt{2}+\frac{25\left(-2\right)}{2}$$

Multiply 25 and -2 to get -50.

$$\frac{875}{2}\sqrt{2}+\frac{-50}{2}$$

Divide -50 by 2 to get -25.

$$\frac{875}{2}\sqrt{2}-25$$

Factor

$$\frac{25 {(35 \sqrt{2} - 2)}}{2} = 593.7184335382291$$