Solve 30div44sqrt{44^2+50^2}

$$30 \div 44 \sqrt{ { 44 }^{ 2 } + { 50 }^{ 2 } }$$

Evaluate

$$\frac{15\sqrt{1109}}{11}\approx 45.411343105$$

Solution Steps

Reduce the fraction \frac{30}{44} to lowest terms by extracting and canceling out 2.

$$\frac{15}{22}\sqrt{44^{2}+50^{2}}$$

Calculate 44 to the power of 2 and get 1936.

$$\frac{15}{22}\sqrt{1936+50^{2}}$$

Calculate 50 to the power of 2 and get 2500.

$$\frac{15}{22}\sqrt{1936+2500}$$

Add 1936 and 2500 to get 4436.

$$\frac{15}{22}\sqrt{4436}$$

Factor 4436=2^{2}\times 1109. Rewrite the square root of the product \sqrt{2^{2}\times 1109} as the product of square roots \sqrt{2^{2}}\sqrt{1109}. Take the square root of 2^{2}.

$$\frac{15}{22}\times 2\sqrt{1109}$$

Express \frac{15}{22}\times 2 as a single fraction.

$$\frac{15\times 2}{22}\sqrt{1109}$$

Multiply 15 and 2 to get 30.

$$\frac{30}{22}\sqrt{1109}$$

Reduce the fraction \frac{30}{22} to lowest terms by extracting and canceling out 2.

$$\frac{15}{11}\sqrt{1109}$$