Question

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$-20$$

Short answer

The square roots of -20 are \( i \sqrt{20} \) and \( -i \sqrt{20} \).

Step-by-step solution

Identify the type of number

The given number is -20, a negative number. Since square roots of negative numbers do not exist in real numbers, its square root will be a complex number.

Find the square roots

The square root of -20 can be found using the formula \( \sqrt{-1} = i \), where i is the imaginary unit. Further, \( \sqrt{-20} = \sqrt{-1*20} = \sqrt{-1} \times \sqrt{20} = i \sqrt{20} \). Hence, the square roots of -20 will be \( i \sqrt{20} \) and \( -i \sqrt{20} \).

Check the results

Upon checking, the square of \( i \sqrt{20} \) and \( -i \sqrt{20} \) is -20. Squaring each root provides: \( (i \sqrt{20})^2=(-i \sqrt{20})^2=-20. \) Hence, this verifies that the square roots are correct.