simplify sqrt(-7)*sqrt(-14) — step-by-step solution

Let's reduce:

\sqrt{-7} \times \sqrt{-14}

ⓘ 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{-7}

i \times \sqrt{7}

\sqrt{-14}

i \times \sqrt{14}

i \times \sqrt{7} \times i \times \sqrt{14}

ⓘ Multiplying powers with the same base adds the exponents:

i \times i

i^{2}

■The product of two square roots is the square root of the product:

\sqrt{7} \times \sqrt{14}

\sqrt{7 \times 14}

i^{2} \times \sqrt{7 \times 14}

ⓘ i^2 = -1, so the powers of i reduce to 1, i, -1 or -i:

i^{2}

-1

■Multiplying by -1 gives the opposite:

-1 \times \sqrt{98}

- \sqrt{98}

ⅰ

7 \times 14

7 \times (10 + 4)

7 \times 10 + 7 \times 4

70 + 28

98

- \sqrt{98}

ⓘ A factor that is an exact power comes out of the root:

- \sqrt{98}

- 7 \times \sqrt{2}

▶Simplified form:

- 7 \times \sqrt{2}

The numeric value of:

- 7 \times \sqrt{2}

is:

- 7 \times \approx 1.4142

▷

\approx -9.8995