What is the square root of 8 simplified?

Answer 1

Square roots, simplified

When you are asked for a simplified square root of some number, the answer is expected to be in radical form, not in decimal form. For example, 3 radical 2 (or three square roots of two) is the simplified square root of 18.

So, let's look at this one: the square root of 8.

The factors of 8 are 4 and 2. (8 and 1 are also factors, but those are not helpful.) So we can say that the square root of 8 is equal to the square root of (4 times 2):

SQT(8) = SQT(4 * 2)

This can be written another way:

SQT(8) = SQT(4) * SQT(2)

Since 4 is a perfect square whose square root is 2, we can write the equation above this way:

SQT(8) = 2 * SQT(2)

In English, that's "The square root of 8 is 2 square roots of 2" or "The square root of 8 is 2 times the square root of 2" or "The square root of 8 is 2 radical 2."

What's this radical business? Well, I can't draw the radical sign here, so I've been using the SQT(x) convention. That is equal to an x under a radical sign.

By the way, 2 times the square root of 2 is 2.828, if you are wondering.