Solve frac{(10sqrt{13}+16)(sqrt{13}+1)}{29}

$$\frac { ( 10 \sqrt { 13 } + 16 ) ( \sqrt { 13 } + 1 ) } { 29 }$$

Evaluate

$$\frac{2\left(13\sqrt{13}+73\right)}{29}\approx 8.267045971$$

Solution Steps

Apply the distributive property by multiplying each term of 10\sqrt{13}+16 by each term of \sqrt{13}+1.

$$\frac{10\left(\sqrt{13}\right)^{2}+10\sqrt{13}+16\sqrt{13}+16}{29}$$

The square of \sqrt{13} is 13.

$$\frac{10\times 13+10\sqrt{13}+16\sqrt{13}+16}{29}$$

Multiply 10 and 13 to get 130.

$$\frac{130+10\sqrt{13}+16\sqrt{13}+16}{29}$$

Combine 10\sqrt{13} and 16\sqrt{13} to get 26\sqrt{13}.

$$\frac{130+26\sqrt{13}+16}{29}$$

Add 130 and 16 to get 146.

$$\frac{146+26\sqrt{13}}{29}$$

Factor

$$\frac{2 {(13 \sqrt{13} + 73)}}{29} = 8.267045971105645$$