Solve 3-sqrt{49+2(3+4^2)div1/2}

$$3 - \sqrt { 49 + 2 ( 3 + 4 ^ { 2 } ) \div 1 / 2 }$$

Evaluate

$$3-5\sqrt{5}\approx -8.180339887$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$3-\sqrt{49+\frac{2\left(3+16\right)}{\frac{1}{2}}}$$

Add 3 and 16 to get 19.

$$3-\sqrt{49+\frac{2\times 19}{\frac{1}{2}}}$$

Multiply 2 and 19 to get 38.

$$3-\sqrt{49+\frac{38}{\frac{1}{2}}}$$

Divide 38 by \frac{1}{2} by multiplying 38 by the reciprocal of \frac{1}{2}.

$$3-\sqrt{49+38\times 2}$$

Multiply 38 and 2 to get 76.

$$3-\sqrt{49+76}$$

Add 49 and 76 to get 125.

$$3-\sqrt{125}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$3-5\sqrt{5}$$