Length of (4, 4, 7)

Step by step

The question

Question: find the length of (4, 4, 7).

The length of v, written with double bars, is Pythagoras in more directions: square every entry, add, then take the square root.

1 Square and add

Every entry squared.

Careful!

The entries are squared first, then added.

Adding the entries themselves is not the length.

The squares: 16 + 16 + 49.

Added: 81.

2 Take the square root

81 is 9 squared.

So the length is 9.

3 Check

Let's check: the length squared must give back 81.

It does.

So the answer is right!

Let's look back.

First: square and add.

Then: take the square root.

Last: check.