Solve 78/111+5^2*sqrt{828%}

$$\frac{ 78 }{ 111 } + { 5 }^{ 2 } \times \sqrt{ 828 \% }$$

Evaluate

$$15\sqrt{23}+\frac{26}{37}\approx 72.640175552$$

Solution Steps

Reduce the fraction \frac{78}{111} to lowest terms by extracting and canceling out 3.

$$\frac{26}{37}+5^{2}\sqrt{\frac{828}{100}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{26}{37}+25\sqrt{\frac{828}{100}}$$

Reduce the fraction \frac{828}{100} to lowest terms by extracting and canceling out 4.

$$\frac{26}{37}+25\sqrt{\frac{207}{25}}$$

Rewrite the square root of the division \sqrt{\frac{207}{25}} as the division of square roots \frac{\sqrt{207}}{\sqrt{25}}.

$$\frac{26}{37}+25\times \frac{\sqrt{207}}{\sqrt{25}}$$

Factor 207=3^{2}\times 23. Rewrite the square root of the product \sqrt{3^{2}\times 23} as the product of square roots \sqrt{3^{2}}\sqrt{23}. Take the square root of 3^{2}.

$$\frac{26}{37}+25\times \frac{3\sqrt{23}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{26}{37}+25\times \frac{3\sqrt{23}}{5}$$

Cancel out 5, the greatest common factor in 25 and 5.

$$\frac{26}{37}+5\times 3\sqrt{23}$$

Multiply 5 and 3 to get 15.

$$\frac{26}{37}+15\sqrt{23}$$

Factor

$$\frac{555 \sqrt{23} + 26}{37} = 72.64017555239349$$