Solve (9)frac{1-sqrt{2}}{2}*frac{1+sqrt{2}}{2}

$$( 9 ) \frac { 1 - \sqrt { 2 } } { 2 } \cdot \frac { 1 + \sqrt { 2 } } { 2 }$$

Evaluate

$$-\frac{9}{4}=-2.25$$

Solution Steps

Express 9\times \frac{1-\sqrt{2}}{2} as a single fraction.

$$\frac{9\left(1-\sqrt{2}\right)}{2}\times \frac{1+\sqrt{2}}{2}$$

Multiply \frac{9\left(1-\sqrt{2}\right)}{2} times \frac{1+\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{9\left(1-\sqrt{2}\right)\left(1+\sqrt{2}\right)}{4}$$

Use the distributive property to multiply 9 by 1-\sqrt{2}.

$$\frac{\left(9-9\sqrt{2}\right)\left(1+\sqrt{2}\right)}{4}$$

Apply the distributive property by multiplying each term of 9-9\sqrt{2} by each term of 1+\sqrt{2}.

$$\frac{9+9\sqrt{2}-9\sqrt{2}-9\left(\sqrt{2}\right)^{2}}{4}$$

Combine 9\sqrt{2} and -9\sqrt{2} to get 0.

$$\frac{9-9\left(\sqrt{2}\right)^{2}}{4}$$

The square of \sqrt{2} is 2.

$$\frac{9-9\times 2}{4}$$

Multiply -9 and 2 to get -18.

$$\frac{9-18}{4}$$

Subtract 18 from 9 to get -9.

$$\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$-\frac{9}{4}$$

Factor

$$-\frac{9}{4} = -2\frac{1}{4} = -2.25$$