Question

`sqrt(5) xx sqrt(90)` is ______.

Options

• `5sqrt(10)`

• `15sqrt(2)`

• `10sqrt(2)`

• `12sqrt(10)`

Answer 1

`sqrt(5) xx sqrt(90)` is `underlinebb(15sqrt(2))`.

Explanation:

Let’s simplify:

`sqrt(5) xx sqrt(90)`

= `sqrt(5 xx 90)`

= `sqrt(450)`

Now, factor 450:

450

= 25 × 18 

= (5²)(3²)(2)

⇒ `sqrt(450)`

= `sqrt(25 xx 9 xx 2)`

= `5 xx 3 xx sqrt(2)`

= `15sqrt(2)`