Solve 7^2+frac{sqrt{436div7}}{444}

$${ 7 }^{ 2 } + \frac{ \sqrt{ 436 \div 7 } }{ 444 }$$

Evaluate

$$\frac{\sqrt{763}}{1554}+49\approx 49.017775067$$

Short Solution Steps

Calculate 7 to the power of 2 and get 49.

$$49+\frac{\sqrt{\frac{436}{7}}}{444}$$

Rewrite the square root of the division \sqrt{\frac{436}{7}} as the division of square roots \frac{\sqrt{436}}{\sqrt{7}}.

$$49+\frac{\frac{\sqrt{436}}{\sqrt{7}}}{444}$$

Factor 436=2^{2}\times 109. Rewrite the square root of the product \sqrt{2^{2}\times 109} as the product of square roots \sqrt{2^{2}}\sqrt{109}. Take the square root of 2^{2}.

$$49+\frac{\frac{2\sqrt{109}}{\sqrt{7}}}{444}$$

Rationalize the denominator of \frac{2\sqrt{109}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$49+\frac{\frac{2\sqrt{109}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}}{444}$$

The square of \sqrt{7} is 7.

$$49+\frac{\frac{2\sqrt{109}\sqrt{7}}{7}}{444}$$

To multiply \sqrt{109} and \sqrt{7}, multiply the numbers under the square root.

$$49+\frac{\frac{2\sqrt{763}}{7}}{444}$$

Express \frac{\frac{2\sqrt{763}}{7}}{444} as a single fraction.

$$49+\frac{2\sqrt{763}}{7\times 444}$$

Cancel out 2 in both numerator and denominator.

$$49+\frac{\sqrt{763}}{7\times 222}$$

Multiply 7 and 222 to get 1554.

$$49+\frac{\sqrt{763}}{1554}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 49 times \frac{1554}{1554}.

$$\frac{49\times 1554}{1554}+\frac{\sqrt{763}}{1554}$$

Since \frac{49\times 1554}{1554} and \frac{\sqrt{763}}{1554} have the same denominator, add them by adding their numerators.

$$\frac{49\times 1554+\sqrt{763}}{1554}$$

Do the multiplications in 49\times 1554+\sqrt{763}.

$$\frac{76146+\sqrt{763}}{1554}$$

Factor

$$\frac{\sqrt{763} + 76146}{1554} = 49.01777506733196$$