Question

Perform the following operations and write the answers in radical form.

Answer 1

Given:

Part A:
`√(7)+√(3)+√(98)-√(18)`

Part B:
`3 √(5)-3 √(11)+2 √(121)-3 √(90)`

To find:

The simplified radical form.

Solution:

Part A:
`√(7)+√(3)+√(98)-√(18)`

`√(98)=√(7^2 * 2) =7 √(2)`

`√(18)=√(3^2 * 2) =3 √(2)`

Substitute these in the given expression.

`√(7)+√(3)+√(98)-√(18)=√(7)+√(3)+7√( 2)-3√( 2)`

Add or subtract the coefficient of same radical.

`=√(7)+√(3)+(7-3)√( 2)`

`=√(7)+√(3)+4√( 2)`

Part B:
`3 √(5)-3 √(11)+2 √(121)-3 √(90)`

`2 √(121)=2√(11^2)`

`=2* 11`

= 22

`3 √(90)=3√(3^2 * 10)`

`=3* 3 √(10)`

`=9 √(10)`

Substitute these in the given expression.

`3 √(5)-3 √(11)+2 √(121)-3 √(90)=3 √(5)-3 √(11)+22-9 √(10)`