Question

HELPPP!! ASAP What is the simplified form of the following expression?

5 sqrt 8 - sqrt 18 - 2 sqrt 2

Answer 1

5
`√(2)`

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplify each radical

5
`√(8)`

= 5
`√(4(2))`

= 5 ×
`√(4)` ×
`√(2)`

= 5 × 2 ×
`√(2)` = 10
`√(2)`

-----------------------------------------------------------

`√(18)`

=
`√(9(2))`

=
`√(9)` ×
`√(2)` = 3
`√(2)`

-----------------------------------------------------------

Putting it all together

10
`√(2)` - 3
`√(2)` - 2
`√(2)`

Collect like terms

=
`√(2)` (10 - 3 - 2 ) = 5
`√(2)`

Answer 2

5 sqrt2.

Explanation:

5 sqrt 8 - sqrt 18 - 2 sqrt 2

= 5 sqrt(4*2) - sqrt(9*2) - 2 sqrt2

= 5 sqrt4*sqrt 2 - sqrt 9*sqrt 2 - 2 sqrt2

= 10 sqrt2 - 3 sqrt2 - 2 sqrt 2

= 5 sqrt2.