# How do you multiply sqrt(2x^6) *sqrt(6x^4)?

It is

$\sqrt{2 {x}^{6}} \cdot \sqrt{6 {x}^{4}} = \sqrt{12 {x}^{10}} = 2 \cdot \sqrt{3} \cdot {\left\mid x \right\mid}^{5}$

Mar 13, 2018

$\sqrt{2 \cdot {x}^{6}} \cdot \sqrt{6 \cdot {x}^{4}} = 3.464 \cdot {x}^{5}$

#### Explanation:

There are 2 basic approaches available.

1st Approach
Do the square roots first.
$\sqrt{2 \cdot {x}^{6}} \cdot \sqrt{6 \cdot {x}^{4}} = \left(1.414 \cdot {x}^{3}\right) \cdot \left(2.449 \cdot {x}^{2}\right)$

$\sqrt{2 \cdot {x}^{6}} \cdot \sqrt{6 \cdot {x}^{4}} = 3.464 \cdot {x}^{3 + 2} = 3.464 \cdot {x}^{5}$

2nd Approach
sqrt(2*x^6) * sqrt(6*x^4) = sqrt(2*6*x^(6+4)

$\sqrt{2 \cdot {x}^{6}} \cdot \sqrt{6 \cdot {x}^{4}} = \sqrt{12 \cdot {x}^{10}} = 3.464 \cdot {x}^{5}$

I hope this helps,
Steve

Mar 13, 2018

With any problem involving the multiplication of two square roots you can use the property $\sqrt{x} \times \sqrt{y} = \sqrt{x y}$

#### Explanation:

Since a square root is equivalent to ${x}^{\frac{1}{2}}$ we can use the exponential laws for square roots.
${a}^{x} {b}^{x} = {\left(a b\right)}^{x}$ --> $\sqrt{x} \times \sqrt{y} = \sqrt{x y}$

$\sqrt{2 {x}^{6}} \times \sqrt{6 {x}^{4}} = \sqrt{2 {x}^{6} \times 6 {x}^{4}} = \sqrt{12 {x}^{10}}$

$\sqrt{12 {x}^{10}}$ can be simplified to ${x}^{5} \times \sqrt{12}$ since $\sqrt{{x}^{10}} = {x}^{5}$

You could also break out a 2 by dividing the inside by 4 (since $\sqrt{4} = 2$) giving you $2 {x}^{5} \sqrt{3}$