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, $sqrt200=sqrt100*sqrt2=10sqrt2$

How do you simplify sqrt10*sqrt20sqrt10*sqrt20?