Question

What is the exact value of the expression the square root of 294 - the square root of 24 + the square root of 54

Answer 1

8
`√(6)`

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` =
`√(ab)`

Simplifying the given radicals

`√(294)`

=
`√(49(6))`

=
`√(49)` ×
`√(6)` = 7
`√(6)`

`√(24)`

=
`√(4(6))`

=
`√(4)` ×
`√(6)` = 2
`√(6)`

`√(54)`

=
`√(9(6))`

=
`√(9)` ×
`√(6)` = 3
`√(6)`

Hence

7
`√(6)` - 2
`√(6)` + 3
`√(6)`

= 8
`√(6)`