Solve sqrt{16^2+(-9^2)+(-14^2)}

$$\sqrt { 16 ^ { 2 } + ( - 9 ^ { 2 } ) + ( - 14 ^ { 2 } ) }$$

Evaluate (complex solution)

$$\sqrt{21}i\approx 4.582575695i$$

Solution Steps

Calculate 16 to the power of 2 and get 256.

$$\sqrt{256-9^{2}-14^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{256-81-14^{2}}$$

Subtract 81 from 256 to get 175.

$$\sqrt{175-14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\sqrt{175-196}$$

Subtract 196 from 175 to get -21.

$$\sqrt{-21}$$

Factor -21=21\left(-1\right). Rewrite the square root of the product \sqrt{21\left(-1\right)} as the product of square roots \sqrt{21}\sqrt{-1}. By definition, the square root of -1 is i.

$$\sqrt{21}i$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Calculate 16 to the power of 2 and get 256.

$$\sqrt{256-9^{2}-14^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\sqrt{256-81-14^{2}}$$

Subtract 81 from 256 to get 175.

$$\sqrt{175-14^{2}}$$

Calculate 14 to the power of 2 and get 196.

$$\sqrt{175-196}$$

Subtract 196 from 175 to get -21.

$$\sqrt{-21}$$

Real Part (complex solution)

$$0$$