a) √8+√18+√32
First factorize each radical term and then simplify.
√8=√2x2x2 =√2 x √2² =2√2
√18=√2x3x3 =√2 x √3² = 3√2
and
√32=√2x4x4=√2x√4² = 4√2
We get
2√2+3√2+4√2
Add similar terms.
=> (2+3+4)√2
=9√2
Answer: 9√2
b)
√98+√50+√72
Factorize each term and then simplify.
√98 =√2x7x7 = √2 x √7² = 7√2
√50 = √2x5x5 = √2 x √5² = 5√2
and
√72=√2x2x2x3x3 = √2² x √3² x √2 = 2x3 √2=6√2
we get
7√2 + 5√2 + 6√2
Add like terms
(7+5+6)√2
= 18√2
Answer: 18√2
c)
√108+ √27 + √75
Factorize each term and simplify.
√108 = √2x2x3x3x3 = √2² x √3² x √3= 2 x 3 x √3 =6√3
√27= √3x3x3 =√3² x √3 = 3√3
and
√75=√3x5x5 = √5² x √3 = 5√3
We get
6√3 + 3√3 + 5√3
Add like terms
(6+3+5)√3
=14√3
Answer: 14√3
