Solve 30+-frac{sqrt{-30^24*5*49}}{2*5}

$$30+- \frac{ \sqrt{ { -30 }^{ 2 } 4 \cdot 5 \cdot 49 } }{ 2 \times 5 }$$

Evaluate

$$30-42\sqrt{5}\approx -63.914855055$$

Solution Steps

Calculate -30 to the power of 2 and get 900.

$$30-\frac{\sqrt{900\times 4\times 5\times 49}}{2\times 5}$$

Multiply 900 and 4 to get 3600.

$$30-\frac{\sqrt{3600\times 5\times 49}}{2\times 5}$$

Multiply 3600 and 5 to get 18000.

$$30-\frac{\sqrt{18000\times 49}}{2\times 5}$$

Multiply 18000 and 49 to get 882000.

$$30-\frac{\sqrt{882000}}{2\times 5}$$

Factor 882000=420^{2}\times 5. Rewrite the square root of the product \sqrt{420^{2}\times 5} as the product of square roots \sqrt{420^{2}}\sqrt{5}. Take the square root of 420^{2}.

$$30-\frac{420\sqrt{5}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$30-\frac{420\sqrt{5}}{10}$$

Divide 420\sqrt{5} by 10 to get 42\sqrt{5}.

$$30-42\sqrt{5}$$

Factor

$$6 \sqrt{5} {(\sqrt{5} - 7)} = -63.914855055$$