Solve frac{270+10(27+sqrt{9*3*23})}{2*27}

$$\frac{ 270+10(27+ \sqrt{ 9 \times 3 \times 23 } ) }{ 2 \times 27 }$$

Evaluate

$$\frac{5\sqrt{69}}{9}+10\approx 14.614791035$$

Solution Steps

Multiply 9 and 3 to get 27.

$$\frac{270+10\left(27+\sqrt{27\times 23}\right)}{2\times 27}$$

Multiply 27 and 23 to get 621.

$$\frac{270+10\left(27+\sqrt{621}\right)}{2\times 27}$$

Factor 621=3^{2}\times 69. Rewrite the square root of the product \sqrt{3^{2}\times 69} as the product of square roots \sqrt{3^{2}}\sqrt{69}. Take the square root of 3^{2}.

$$\frac{270+10\left(27+3\sqrt{69}\right)}{2\times 27}$$

Multiply 2 and 27 to get 54.

$$\frac{270+10\left(27+3\sqrt{69}\right)}{54}$$

Use the distributive property to multiply 10 by 27+3\sqrt{69}.

$$\frac{270+270+30\sqrt{69}}{54}$$

Add 270 and 270 to get 540.

$$\frac{540+30\sqrt{69}}{54}$$

Factor

$$\frac{5 {(\sqrt{69} + 18)}}{9} = 14.614791034954484$$