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

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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