Question

How you simplify (Square root of 75) +(square root of 48)?

Answer 1

`= color(blue)(9sqrt3`

Explanation:

• Square root of a number can be simplified by prime factorising the number.

• Prime factorisation involves expressing a number as a product of prime numbers.

(`75` has `3` and `5` as its prime factors and `48` has `2` and `3` as its prime factors)

So,
`sqrt75=sqrt(5*5*3) = sqrt(5^2*3) = 5sqrt3`

`sqrt48=sqrt(2*2*2*2*3)= sqrt(2^2*2^2*3) = 4sqrt3`

Now,
`sqrt75 +sqrt48 = 5sqrt3+4sqrt3 = color(blue)(9sqrt3`