Solve 277+57sqrt{25*78div48}

$$277+57 \sqrt{ 25 \times 78 \div 48 }$$

Evaluate

$$\frac{285\sqrt{26}}{4}+277\approx 640.305140343$$

Short Solution Steps

Multiply 25 and 78 to get 1950.

$$277+57\sqrt{\frac{1950}{48}}$$

Reduce the fraction \frac{1950}{48} to lowest terms by extracting and canceling out 6.

$$277+57\sqrt{\frac{325}{8}}$$

Rewrite the square root of the division \sqrt{\frac{325}{8}} as the division of square roots \frac{\sqrt{325}}{\sqrt{8}}.

$$277+57\times \frac{\sqrt{325}}{\sqrt{8}}$$

Factor 325=5^{2}\times 13. Rewrite the square root of the product \sqrt{5^{2}\times 13} as the product of square roots \sqrt{5^{2}}\sqrt{13}. Take the square root of 5^{2}.

$$277+57\times \frac{5\sqrt{13}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$277+57\times \frac{5\sqrt{13}}{2\sqrt{2}}$$

Rationalize the denominator of \frac{5\sqrt{13}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$277+57\times \frac{5\sqrt{13}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$277+57\times \frac{5\sqrt{13}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{13} and \sqrt{2}, multiply the numbers under the square root.

$$277+57\times \frac{5\sqrt{26}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$277+57\times \frac{5\sqrt{26}}{4}$$

Express 57\times \frac{5\sqrt{26}}{4} as a single fraction.

$$277+\frac{57\times 5\sqrt{26}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 277 times \frac{4}{4}.

$$\frac{277\times 4}{4}+\frac{57\times 5\sqrt{26}}{4}$$

Since \frac{277\times 4}{4} and \frac{57\times 5\sqrt{26}}{4} have the same denominator, add them by adding their numerators.

$$\frac{277\times 4+57\times 5\sqrt{26}}{4}$$

Do the multiplications in 277\times 4+57\times 5\sqrt{26}.

$$\frac{1108+285\sqrt{26}}{4}$$