Question

How do you simplify `sqrt10*sqrt20`?

Answer 1

`10sqrt2`

Explanation:

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

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

Explanation:

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`