Solve [15/2(sqrt{2}+1)]^2

$$[ \frac { 15 } { 2 } ( \sqrt { 2 } + 1 ) ] ^ { 2 }$$

Evaluate

$$\frac{225\left(2\sqrt{2}+3\right)}{4}\approx 327.849025767$$

Solution Steps

Use the distributive property to multiply \frac{15}{2} by \sqrt{2}+1.

$$\left(\frac{15}{2}\sqrt{2}+\frac{15}{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{15}{2}\sqrt{2}+\frac{15}{2}\right)^{2}.

$$\frac{225}{4}\left(\sqrt{2}\right)^{2}+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

The square of \sqrt{2} is 2.

$$\frac{225}{4}\times 2+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

Multiply \frac{225}{4} and 2 to get \frac{225}{2}.

$$\frac{225}{2}+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

Add \frac{225}{2} and \frac{225}{4} to get \frac{675}{4}.

$$\frac{675}{4}+\frac{225}{2}\sqrt{2}$$

Expand

$$\frac{225 \sqrt{2}}{2} + \frac{675}{4} = 327.849025767$$

Solution Steps

Use the distributive property to multiply \frac{15}{2} by \sqrt{2}+1.

$$\left(\frac{15}{2}\sqrt{2}+\frac{15}{2}\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{15}{2}\sqrt{2}+\frac{15}{2}\right)^{2}.

$$\frac{225}{4}\left(\sqrt{2}\right)^{2}+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

The square of \sqrt{2} is 2.

$$\frac{225}{4}\times 2+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

Multiply \frac{225}{4} and 2 to get \frac{225}{2}.

$$\frac{225}{2}+\frac{225}{2}\sqrt{2}+\frac{225}{4}$$

Add \frac{225}{2} and \frac{225}{4} to get \frac{675}{4}.

$$\frac{675}{4}+\frac{225}{2}\sqrt{2}$$