How do you simplify the square root of 196?

To simplify the square root of 196, you can factorize the number under the square root sign and look for perfect square factors. In this case, 196 is a perfect square since it can be expressed as the square of a whole number.

The prime factorization of 196 is:

196 = 2 * 2 * 7 * 7

Now, group the factors into pairs, where each pair consists of two identical factors:

196 = (2 * 2) * (7 * 7)

Simplifying further:

196 = 4 * 49

Since both 4 and 49 are perfect squares, we can simplify:

196 = (2^2) * (7^2)

Taking the square root:

√196 = √(2^2 * 7^2)

Using the property of square roots, we can split the square root:

√196 = √(2^2) * √(7^2)

Simplifying:

√196 = 2 * 7

√196 = 14

Therefore, the simplified square root of 196 is 14.