Solve sqrt{10^2-17*3*3-27^0}

$$\sqrt { 10 ^ { 2 } - 17 \cdot 3 \cdot 3 - 27 ^ { 0 } }$$

Evaluate (complex solution)

$$3\sqrt{6}i\approx 7.348469228i$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\sqrt{100-17\times 3\times 3-27^{0}}$$

Multiply 17 and 3 to get 51.

$$\sqrt{100-51\times 3-27^{0}}$$

Multiply 51 and 3 to get 153.

$$\sqrt{100-153-27^{0}}$$

Subtract 153 from 100 to get -53.

$$\sqrt{-53-27^{0}}$$

Calculate 27 to the power of 0 and get 1.

$$\sqrt{-53-1}$$

Subtract 1 from -53 to get -54.

$$\sqrt{-54}$$

Factor -54=\left(3i\right)^{2}\times 6. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 6} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{6}. Take the square root of \left(3i\right)^{2}.

$$3i\sqrt{6}$$

Real Part (complex solution)

$$0$$

Evaluate

$$\text{Indeterminate}$$