Question

How do you simplify `sqrt(1,440)`?

Answer 1

`12sqrt10`

Explanation:

`"note that " 1440=144xx10" and 144 is a perfect square"`

`"using the "color(blue)"law of radicals"`

`•color(white)(x)sqrt(ab)=sqrtaxxsqrtb`

`rArrsqrt1440=sqrt(144xx10)`

`color(white)(xxxxxxx)=sqrt144xxsqrt10=12sqrt10`

Answer 2

`12sqrt10`

Explanation:

When you are simplifying radicals, you need to find two numbers. Between those two numbers, one HAS to be a perfect square, or it does not simplify.

Here, we are given:

`sqrt1440`

We can see here that there is an easy and more noticeable factorization:

`sqrt144 * sqrt10`

Thankfully, `144` is perfect square, so `sqrt144` can be reduced to `12`. Since `10` does not divide evenly into any prefect squares, `sqrt10` will no simplify.

Therefore, are answer will be:

`12sqrt10`