Multiply Radicals

Combine 6x and 3x³y
in a square root sign.

So √6x × √3x³y = √6x⋅3x³y.

6 = 2⋅3

3⋅3 = 3²
x⋅x³ = x^{1 + 3} = x⁴

Product of Powers

Change the factors of 2⋅3²⋅x⁴⋅y to perfect squares
as much as you can.

3² is already a perfect square.

x⁴
= x^2⋅2
= (x²)²

Power of a Power

Take the squared factors, 3 and x²,
out from the square root.

And leave the non-squared factors, 2 and y,
in the square root.

Simplify a Radical

So 3x²√2y is the answer.

Use the FOIL method.

Multiply the first two terms: √3⋅√6.
Multiply the outer terms: √3⋅(-2) = -2√3.
Multiply the inner terms: +√2⋅√6.
Multiply the last two terms: +√2⋅(-2) = -2√2.

Split √6 into √3 and √2:
√6 = √3⋅√2.

√3⋅√3
= (√3)²
= 3

√2⋅√2
= (√2)²
= 2

Square Root

Cancel -2√3 and +2√3.
And 3√2 - 2√2 = √2.

So 3√2 - 2√3 + 2√3 - 2√2 = √2.

Add and Subtract Radicals

So √2 is the answer.