How do you simplify #sqrt10*sqrt20#?

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Answer 1 · 2017-01-24T15:44:04

#10sqrt2#

Using the property that states that #sqrtasqrtb = sqrt(ab)#,

#sqrt10 * sqrt20 = sqrt(10 * 20) = sqrt200 = sqrt(25 * 4 * 2)#

#=sqrt25sqrt4sqrt2 = 5 * 2 * sqrt2 = 10sqrt2#.

Answer 2 · 2017-01-24T15:45:37

Multiply the two radicals together, then simplify the result. Details below...
The result is #10sqrt2#

First, since square root is the same as using the exponent #1/2# the two radicals obey the rule

#a^x*b^x=(a*b)^x#

So #10^(1/2)*20^(1/2) = 200^(1/2)# or #sqrt200#

Next, look for the largest factor of 200 that is a perfect square. This is #100 xx 2#

So, #sqrt200=sqrt100*sqrt2=10sqrt2#