Question

16 divide root 2 -35 divide root 50 -2 root 18 + 3 root 72​

Answer 1

Given:

The expression is:

`(16)/(√(2))-(35)/(√(50))-2√(18)+3√(72)`

To find:

The simplified form of the given expression.

Solution:

We have,

`(16)/(√(2))-(35)/(√(50))-2√(18)+3√(72)`

It can be written as:

`=(16)/(√(2))-(35)/(√(25* 2))-2√(9* 2)+3√(36* 2)`

`=(16)/(√(2))-(35)/(5√(2))-2* 3√(2)+3* 6√(2)`

Rationalizing the denominator, we get

`=(16)/(√(2))* (√(2))/(√(2))-(35)/(5√(2))* (√(2))/(√(2))-6√(2)+18√(2)`

`=(16√(2))/(2)-(35√(2))/(5* 2)-6√(2)+18√(2)`

`=8√(2)-(7√(2))/(2)+12√(2)`

`=20√(2)-(7√(2))/(2)`

Taking LCM, we get

`=(40√(2)-7√(2))/(2)`

`=(33√(2))/(2)`

Therefore, the simplified form of the given expression is
`(33√(2))/(2)`.