How do you simplify the square root of 18 minus the square root of 50?

| May 27, 2018

You check to see what you can extract from those radicals.
You expression looks like this
##sqrt(18) – sqrt(50)##
Write the prime factors of these two numbers to see if you can find write tham as products of a perfect square and another number
##18 = 2 * 9 = 2 * 3 * 3 = 2 * 3^2##
##50 = 2 * 25 = 2 * 5 * 5 = 2 * 5^2##
You can thus write, with the help of the product property of radicals, an equivalent expression that looks like this
##sqrt(2 * 3^2) – sqrt(2 * 5^2) = sqrt(2) * sqrt(3^2) – sqrt(2) * sqrt(5^2)##
Finally, you get
##3 * sqrt(2) – 5 * sqrt(2) = color(green)(-2sqrt(2))##

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