Solve sqrt{(6+i)(6-i)}

$$\sqrt { ( 6 + i ) ( 6 - i ) }$$

Evaluate

$$\sqrt{37}\approx 6.08276253$$

Solution Steps

Multiply complex numbers 6+i and 6-i like you multiply binomials.

$$\sqrt{6\times 6+6\left(-i\right)+6i-i^{2}}$$

By definition, i^{2} is -1.

$$\sqrt{6\times 6+6\left(-i\right)+6i-\left(-1\right)}$$

Do the multiplications in 6\times 6+6\left(-i\right)+6i-\left(-1\right).

$$\sqrt{36-6i+6i+1}$$

Combine the real and imaginary parts in 36-6i+6i+1.

$$\sqrt{36+1+\left(-6+6\right)i}$$

Do the additions in 36+1+\left(-6+6\right)i.

$$\sqrt{37}$$

Real Part

$$\sqrt{37} = 6.08276253$$