Solve frac{5*sqrt{2}}{2}*(sqrt{2}-1)1^2

$$\frac{ 5 \times \sqrt{ 2 } }{ 2 } \times ( \sqrt{ 2 } -1) { 1 }^{ 2 }$$

Evaluate

$$-\frac{5\sqrt{2}}{2}+5\approx 1.464466094$$

Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{5\sqrt{2}}{2}\left(\sqrt{2}-1\right)\times 1$$

Express \frac{5\sqrt{2}}{2}\left(\sqrt{2}-1\right) as a single fraction.

$$\frac{5\sqrt{2}\left(\sqrt{2}-1\right)}{2}\times 1$$

Express \frac{5\sqrt{2}\left(\sqrt{2}-1\right)}{2}\times 1 as a single fraction.

$$\frac{5\sqrt{2}\left(\sqrt{2}-1\right)}{2}$$

Use the distributive property to multiply 5\sqrt{2} by \sqrt{2}-1.

$$\frac{5\left(\sqrt{2}\right)^{2}-5\sqrt{2}}{2}$$

The square of \sqrt{2} is 2.

$$\frac{5\times 2-5\sqrt{2}}{2}$$

Multiply 5 and 2 to get 10.

$$\frac{10-5\sqrt{2}}{2}$$