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

1 Answer
Jul 27, 2015

Answer:

#= 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#