What is the square root of 8 times the square root of 20?

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Answer 1 · 2018-06-27T12:29:19

See a solution process below:

We can rewrite the expression:

#sqrt(8) xx sqrt(20)#

using the following rule for radicals:

#sqrt(color(red)(a)) * sqrt(color(blue)(b)) = sqrt(color(red)(a) * color(blue)(b))#

#sqrt(color(red)(8)) * sqrt(color(blue)(20)) => sqrt(color(red)(8) * color(blue)(20)) => sqrt(160)#

Now, we can use this rule for radicals to simplify the radical:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#sqrt(160) => sqrt(color(red)(16) * color(blue)(10)) => sqrt(color(red)(16)) * sqrt(color(blue)(10)) => 4sqrt(10)#