simplify sqrt(-108)-sqrt(-3) — step-by-step solution

Let's simplify:

\sqrt{-108} - \sqrt{-3}

ⓘ In ℂ, the principal square root of a negative real number is i times the square root of its absolute value, because i² = -1:

\sqrt{-108}

i \times 6 \times \sqrt{3}

\sqrt{-3}

i \times \sqrt{3}

i \times 6 \times \sqrt{3} - i \times \sqrt{3}

ⓘ Like terms are grouped by adding their coefficients:

i \times 6 \times \sqrt{3} - i \times \sqrt{3}

5 i \times \sqrt{3}

▶Simplified form:

5 i \times \sqrt{3}

The numeric value of:

5 i \times \sqrt{3}

is:

5 i \times \approx 1.7321

▷

\approx 8.6603 i