Solve =1/2sqrt{(-4)^2+9^2+1^2}

$$= \frac { 1 } { 2 } \sqrt { ( - 4 ) ^ { 2 } + 9 ^ { 2 } + 1 ^ { 2 } }$$

Evaluate

$$\frac{7\sqrt{2}}{2}\approx 4.949747468$$

Solution Steps

Calculate -4 to the power of 2 and get 16.

$$\frac{1}{2}\sqrt{16+9^{2}+1^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{1}{2}\sqrt{16+81+1^{2}}$$

Add 16 and 81 to get 97.

$$\frac{1}{2}\sqrt{97+1^{2}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{1}{2}\sqrt{97+1}$$

Add 97 and 1 to get 98.

$$\frac{1}{2}\sqrt{98}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$\frac{1}{2}\times 7\sqrt{2}$$

Multiply \frac{1}{2} and 7 to get \frac{7}{2}.

$$\frac{7}{2}\sqrt{2}$$