Solve -103/sqrt{1660-5*18^2sqrt{10535-5*45.4^2}}

$$\frac { - 103 } { \sqrt { 1660 - 5 \times 18 ^ { 2 } } \sqrt { 10535 - 5 \times 45.4 ^ { 2 } } }$$

Evaluate

$$-\frac{103\sqrt{573}}{2292}\approx -1.075721682$$

Solution Steps

Calculate 18 to the power of 2 and get 324.

$$\frac{-103}{\sqrt{1660-5\times 324}\sqrt{10535-5\times 45.4^{2}}}$$

Multiply 5 and 324 to get 1620.

$$\frac{-103}{\sqrt{1660-1620}\sqrt{10535-5\times 45.4^{2}}}$$

Subtract 1620 from 1660 to get 40.

$$\frac{-103}{\sqrt{40}\sqrt{10535-5\times 45.4^{2}}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{-103}{2\sqrt{10}\sqrt{10535-5\times 45.4^{2}}}$$

Calculate 45.4 to the power of 2 and get 2061.16.

$$\frac{-103}{2\sqrt{10}\sqrt{10535-5\times 2061.16}}$$

Multiply 5 and 2061.16 to get 10305.8.

$$\frac{-103}{2\sqrt{10}\sqrt{10535-10305.8}}$$

Subtract 10305.8 from 10535 to get 229.2.

$$\frac{-103}{2\sqrt{10}\sqrt{229.2}}$$

To multiply \sqrt{10} and \sqrt{229.2}, multiply the numbers under the square root.

$$\frac{-103}{2\sqrt{2292}}$$

Rationalize the denominator of \frac{-103}{2\sqrt{2292}} by multiplying numerator and denominator by \sqrt{2292}.

$$\frac{-103\sqrt{2292}}{2\left(\sqrt{2292}\right)^{2}}$$

The square of \sqrt{2292} is 2292.

$$\frac{-103\sqrt{2292}}{2\times 2292}$$

Factor 2292=2^{2}\times 573. Rewrite the square root of the product \sqrt{2^{2}\times 573} as the product of square roots \sqrt{2^{2}}\sqrt{573}. Take the square root of 2^{2}.

$$\frac{-103\times 2\sqrt{573}}{2\times 2292}$$

Multiply -103 and 2 to get -206.

$$\frac{-206\sqrt{573}}{2\times 2292}$$

Multiply 2 and 2292 to get 4584.

$$\frac{-206\sqrt{573}}{4584}$$

Divide -206\sqrt{573} by 4584 to get -\frac{103}{2292}\sqrt{573}.

$$-\frac{103}{2292}\sqrt{573}$$