# distance formula: simplifying sqrt(148)

#### marshall1432

##### Banned
i have a small question...regarding the distance formula...

(-7, 1) (5,3)

using the distance formula.....sqrt(x2-x1)+(y2-y1)...I was able to determine that the answer is sqrt(148)

How do I go about getting the final answer or is this...I am unsure, but I think it stays this way...

I don't need it in a decimal

#### Mrspi

##### Senior Member
Re: distance formula

marshall1432 said:
i have a small question...regarding the distance formula...

(-7, 1) (5,3)

using the distance formula.....sqrt(x2-x1)+(y2-y1)...I was able to determine that the answer is sqrt(148)

How do I go about getting the final answer or is this...I am unsure, but I think it stays this way...

I don't need it in a decimal
You need to see if you can simplify sqrt(148)

Does 148 have any perfect square factors? If so, you can remove the square root of any perfect square factor from under the radical sign.

Here's an example:

Simplify sqrt(60)

Note that 60 = 4*15, and that 4 is a perfect square. So,

sqrt(60) = sqrt(4*15), or sqrt(4)*sqrt(15)

Now, you know that sqrt(4) is 2, so sqrt(4)*sqrt(15) can be written as 2 sqrt(15).

And sqrt(60 = 2 sqrt(15).

Since 15 does not have any perfect square factors, this is the simplest form for sqrt(60).

Try the same process on sqrt(148).

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: distance formula

marshall1432 said:
i have a small question...regarding the distance formula...

(-7, 1) (5,3)

using the distance formula.....sqrt(x2-x1)+(y2-y1)...I was able to determine that the answer is sqrt(148)

How do I go about getting the final answer or is this...I am unsure, but I think it stays this way...

I don't need it in a decimal
This is good enough in my view.

However, you can reduce it one step further by factorizing148 and taking some factor/s out-of-the radical sign. That is

$$\displaystyle \sqrt{50} \,=\, \sqrt{5^2\cdot2} \, = \,5\sqrt{2}$$

#### marshall1432

##### Banned
Re: distance formula

well there is a perfect square being sqrt 4 * sqrt 37

so would you consider the answer to be 2 sqrt 37?

#### Subhotosh Khan

##### Super Moderator
Staff member
Re: distance formula

marshall1432 said:
well there is a perfect square being sqrt 4 * sqrt 37

so would you consider the answer to be 2 sqrt 37<<<<< Correct
?