Question

Find all square roots of the number or write no square roots. Check the results by squaring each root. $$12$$

Short answer

The square roots of the number 12 are approximately \(\sqrt{12} \approx 3.46\) and \(- \sqrt{12} \approx -3.46\).

Step-by-step solution

Identifying the given number

The given number is 12. Since this number is not a perfect square, it will have irrational square roots.

Calculating the square roots

To find the positive square root of 12, one needs to take the square root of the number using a calculator or mathematical software. Here is the output for the square root of 12: \(\sqrt{12} \approx 3.46\). To find the negative square root, simply take the negative of the positive square root: \(- \sqrt{12} \approx -3.46\).

Checking the calculated square roots

To check the veracity of these square roots, square each root to see if the original number 12 is obtained. Squaring \(\sqrt{12} \approx 3.46\) and \(- \sqrt{12} \approx -3.46\) result in the number approximately 12, which is correct because the square of the root of a number is the number itself.