Solve 7^2+3/8sqrt{58}5

$${ 7 }^{ 2 } + \frac{ 3 }{ 8 \sqrt{ 58 } } 5$$

Evaluate

$$\frac{15\sqrt{58}}{464}+49\approx 49.246199562$$

Short Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49+5\times \frac{3}{8\sqrt{58}}$$

Rationalize the denominator of \frac{3}{8\sqrt{58}} by multiplying numerator and denominator by \sqrt{58}.

$$49+5\times \frac{3\sqrt{58}}{8\left(\sqrt{58}\right)^{2}}$$

The square of \sqrt{58} is 58.

$$49+5\times \frac{3\sqrt{58}}{8\times 58}$$

Multiply 8 and 58 to get 464.

$$49+5\times \frac{3\sqrt{58}}{464}$$

Express 5\times \frac{3\sqrt{58}}{464} as a single fraction.

$$49+\frac{5\times 3\sqrt{58}}{464}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 49 times \frac{464}{464}.

$$\frac{49\times 464}{464}+\frac{5\times 3\sqrt{58}}{464}$$

Since \frac{49\times 464}{464} and \frac{5\times 3\sqrt{58}}{464} have the same denominator, add them by adding their numerators.

$$\frac{49\times 464+5\times 3\sqrt{58}}{464}$$

Do the multiplications in 49\times 464+5\times 3\sqrt{58}.

$$\frac{22736+15\sqrt{58}}{464}$$

Factor

$$\frac{15 \sqrt{58} + 22736}{464} = 49.24619956161198$$