How do you multiply $\sqrt{2 x^{6}} \cdot \sqrt{6 x^{4}}$ $sqrt(2x^6) *sqrt(6x^4)$ ?

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How do you multiply $\sqrt{2 x^{6}} \cdot \sqrt{6 x^{4}}$ $sqrt(2x^6) *sqrt(6x^4)$ ?

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Answer 1 · 2018-03-13T20:18:34

It is

$\sqrt{2 x^{6}} \cdot \sqrt{6 x^{4}} = \sqrt{12 x^{10}} = 2 \cdot \sqrt{3} \cdot {| x |}^{5}$ $sqrt(2x^6)*sqrt(6x^4)=sqrt(12x^10)=2*sqrt3*absx^5$

Answer 2 · 2018-03-13T20:31:32

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

Explanation:

There are 2 basic approaches available.

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

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

2nd Approach
Combine the 2 radicals first.
$\sqrt{2 \cdot x^{6}} \cdot \sqrt{6 \cdot x^{4}} = \sqrt{2 \cdot 6 \cdot x^{6 + 4}}$ $sqrt(2*x^6) * sqrt(6*x^4) = sqrt(2*6*x^(6+4)$

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

I hope this helps,
Steve

Answer 3 · 2018-03-13T20:37:44

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

Explanation:

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

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

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

You could also break out a 2 by dividing the inside by 4 (since $\sqrt{4} = 2$ $sqrt4 =2$ ) giving you $2 x^{5} \sqrt{3}$ $2x^5sqrt3$

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How do you multiply $\sqrt{2 x^{6}} \cdot \sqrt{6 x^{4}}$ $sqrt(2x^6) *sqrt(6x^4)$ ?

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