Which expression is equivalent to √50?

Step by step

The question

Question: which expression is equivalent to √50?

Equivalent means: the same value for every x.

Simplify means: take every square number out from under the root.

There are four choices.

First we simplify it, the normal way.

Then we pick.

1 Find the biggest square number

Square numbers are a number times itself: 2 × 2 = 4, 3 × 3 = 9, and so on.

We want one that goes into 50.

A number that goes in, other than 50 itself, is at most half of it.

So we list them up to half of 50.

We try the biggest first.

Does 25 go into 50?

Yes: 50 divided by 25 is 2.

2 Split the root

So 50 is 25 times 2.

We write it under the root.

Rule: when two numbers are multiplied under a root, we can split it into two roots.

So √(25 × 2) is √25 times √2.

√25 is 5, because 5 times 5 is 25.

We write 5 in place of √25.

We leave out the times sign: 5√2 means 5 times √2.

2 has no square number in it, so we are done.

So √50 = 5√2.

3 Check

Let's check.

√50 times √50 is 50.

So the answer times itself must give 50 too.

Squared means times itself.

5 × 5 is 25, and √2 × √2 is 2.

25 × 2 is 50.

We get 50.

So 5√2 is right!

4 Pick the choice

Our answer is 5√2.

That is choice B.

5 Why not the others

A is 2√5.

Wrong: 50 = 25 × 2, and it is the 25 that comes out, as 5.

C is 10√5.

Wrong: 50 = 10 × 5, but 10 is not a square number.

D is 25√2.

Wrong: the 25 came out as 25: √25 is 5.

Let's look back.

First: find the biggest square number.

Then: split the root.

Then: check.

Then: pick the choice.

Last: why not the others.