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

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Answer 1 · 2015-07-25T12:10:20

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))#