Question

What is the simplified form of the following expression?

Answer 1

You have sqrt(8), sqrt(18), and sqrt(2).
You need to simplify the radicals.
sqrt(2) is already simplified.
For both sqrt(8) and sqrt(18), you need to factor out the greatest perfect square.

8 = 4 * 2
You can take the square root of 4 and put it outside the root.

18 = 9 * 2
You can take the square root of 9 and put it outside the root.


`5 √(8) - √(18) -2 √(2) =`


`= 5 √(4 * 2) - √(9 * 2) -2 √(2)`


`= 5 * 2√(2) - 3 √(2) -2 √(2)`


`= 10√(2) - 3 √(2) -2 √(2)`


`= 5√(2)`

Answer 2

`5\sqrt2`

Explanation:

We are given that an expression

`5\sqrt8-√(18)-2\sqrt2`

We have to simplify the given expression.

Factorize each term

`5√(2* 2* 2)-√(2* 3* 3)-2\sqrt2`

`5* 2\sqrt2-3\sqrt2-2\sqrt2`

`10\sqrt2-3\sqrt2-2\sqrt2`

By simplification

`10\sqrt2-5\sqrt2`

Taking common
`\sqrt2` form each term

`(10-5)\sqrt2`

`5\sqrt2` ( by simplification)

Hence,
`5\sqrt8-√(18)-2\sqrt2=5\sqrt2`