How do you simplify #sqrt1250-sqrt50#?

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Answer 1 · 2015-09-21T03:29:41

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

#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#