Solve (frac{3-sqrt{9}}{sqrt{2}}+frac{4+sqrt{9}}{sqrt{2}})^2

$$( \frac { 3 - \sqrt { 9 } } { \sqrt { 2 } } + \frac { 4 + \sqrt { 9 } } { \sqrt { 2 } } ) ^ { 2 }$$

Evaluate

$$\frac{49}{2}=24.5$$

Solution Steps

Calculate the square root of 9 and get 3.

$$\left(\frac{3-3}{\sqrt{2}}+\frac{4+\sqrt{9}}{\sqrt{2}}\right)^{2}$$

Subtract 3 from 3 to get 0.

$$\left(\frac{0}{\sqrt{2}}+\frac{4+\sqrt{9}}{\sqrt{2}}\right)^{2}$$

Zero divided by any non-zero term gives zero.

$$\left(0+\frac{4+\sqrt{9}}{\sqrt{2}}\right)^{2}$$

Calculate the square root of 9 and get 3.

$$\left(0+\frac{4+3}{\sqrt{2}}\right)^{2}$$

Add 4 and 3 to get 7.

$$\left(0+\frac{7}{\sqrt{2}}\right)^{2}$$

Rationalize the denominator of \frac{7}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\left(0+\frac{7\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\right)^{2}$$

The square of \sqrt{2} is 2.

$$\left(0+\frac{7\sqrt{2}}{2}\right)^{2}$$

Anything plus zero gives itself.

$$\left(\frac{7\sqrt{2}}{2}\right)^{2}$$

To raise \frac{7\sqrt{2}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(7\sqrt{2}\right)^{2}}{2^{2}}$$

Expand \left(7\sqrt{2}\right)^{2}.

$$\frac{7^{2}\left(\sqrt{2}\right)^{2}}{2^{2}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{49\left(\sqrt{2}\right)^{2}}{2^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{49\times 2}{2^{2}}$$

Multiply 49 and 2 to get 98.

$$\frac{98}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{98}{4}$$

Reduce the fraction \frac{98}{4} to lowest terms by extracting and canceling out 2.

$$\frac{49}{2}$$

Factor

$$\frac{7 ^ {2}}{2} = 24\frac{1}{2} = 24.5$$