How do you simplify #4sqrt2*5sqrt8#?

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Answer 1 · 2017-04-20T12:42:49

See the entire solution process below:

The rule for multiplying radicals is:

#sqrt(a) * sqrt(b) = sqrt(a * b)#

Using this rule, rewrite this expression as:

#(4 * 5)(sqrt(2) * sqrt(8)) => 20sqrt(2 * 8) = 20sqrt(16)#

Now, take the square root of 16 remembering the square root of a number produces a negative and positive result:

Solution 1)

#20sqrt(16) => 20 * -4 => -80#

Solution 2)

#20sqrt(16) => 20 * 4 => 80#

The solution is #+-80#