How do you simplify #sqrt1250-sqrt50#?

1 Answer
Sep 21, 2015

Answer:

#sqrt1250-sqrt50 = color(green)(20sqrt2#

Explanation:

#sqrt1250-sqrt50#

# = sqrt(25*25*2) - sqrt(25*2)#

# = sqrt(25^2*2) - sqrt(5^2*2)#

We know that #color(blue)(sqrt(a*b) = sqrta*sqrtb#

#= {sqrt(25^2)*sqrt2} - {sqrt(5^2)*sqrt2}#

# = 25sqrt2 - 5sqrt2#

# = (25-5)sqrt2#

# = color(green)(20sqrt2#