What is the square root of 90 - square root of 10?

1 Answer
Sep 8, 2015

Answer:

Assuming we are dealing only with primary (positive) square roots:
#sqrt(90)-sqrt(10) = 2sqrt(10#

Explanation:

#sqrt(90)#
#color(white)("XX") = sqrt(3^2xx10)#

#color(white)("XX") = sqrt(3^2)*sqrt(10)#

#color(white)("XX") = 3sqrt(10)#

#sqrt(90) -sqrt(10)#

#color(white)("XX") = (3*sqrt(10))-(1*sqrt(10))#

#color(white)("XX") = 2*sqrt(10)#

If we accept both positive and negative values for the square roots, possible solutions include:
#4sqrt(10), -2sqrt(10), and -4sqrt(10)#