Simplify square root of 8xy^4* square root of 2x^2y^4

$\sqrt{8 x y^{4}} \cdot \sqrt{2 x^{2} y^{4}}$

Step 1

Rewrite $8 x y^{4}$ as ${(2 y^{2})}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2) x y^{4}} \cdot \sqrt{2 x^{2} y^{4}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 2 x y^{4}} \cdot \sqrt{2 x^{2} y^{4}}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$\sqrt{2^{2} \cdot 2 x {(y^{2})}^{2}} \cdot \sqrt{2 x^{2} y^{4}}$

Move $x$ .

$\sqrt{2^{2} \cdot 2 {(y^{2})}^{2} x} \cdot \sqrt{2 x^{2} y^{4}}$

Move $2$ .

$\sqrt{2^{2} {(y^{2})}^{2} \cdot 2 x} \cdot \sqrt{2 x^{2} y^{4}}$

Rewrite $2^{2} {(y^{2})}^{2}$ as ${(2 y^{2})}^{2}$ .

$\sqrt{{(2 y^{2})}^{2} \cdot 2 x} \cdot \sqrt{2 x^{2} y^{4}}$

Add parentheses.

$\sqrt{{(2 y^{2})}^{2} \cdot (2 x)} \cdot \sqrt{2 x^{2} y^{4}}$

Step 2

Pull terms out from under the radical.

$2 y^{2} \sqrt{2 x} \cdot \sqrt{2 x^{2} y^{4}}$

Step 3

Rewrite $2 x^{2} y^{4}$ as ${(x y^{2})}^{2} \cdot 2$ .

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$2 y^{2} \sqrt{2 x} \cdot \sqrt{2 x^{2} {(y^{2})}^{2}}$

Move $2$ .

$2 y^{2} \sqrt{2 x} \cdot \sqrt{x^{2} {(y^{2})}^{2} \cdot 2}$

Rewrite $x^{2} {(y^{2})}^{2}$ as ${(x y^{2})}^{2}$ .

$2 y^{2} \sqrt{2 x} \cdot \sqrt{{(x y^{2})}^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$2 y^{2} \sqrt{2 x} \cdot (x y^{2} \sqrt{2})$

Step 5

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$2 (y^{2} y^{2}) \sqrt{2 x} \cdot (x \sqrt{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y^{2 + 2} \sqrt{2 x} \cdot (x \sqrt{2})$

Add $2$ and $2$ .

$2 y^{4} \sqrt{2 x} \cdot (x \sqrt{2})$

Step 6

Multiply $2 y^{4} \sqrt{2 x} (x \sqrt{2})$ .

Combine using the product rule for radicals.

$2 y^{4} (x \sqrt{2 x \cdot 2})$

Multiply $2$ by $2$ .

$2 y^{4} (x \sqrt{4 x})$

Step 7

Rewrite $4$ as $2^{2}$ .

$2 y^{4} (x \sqrt{2^{2} x})$

Step 8

Pull terms out from under the radical.

$2 y^{4} (x (2 \sqrt{x}))$

Step 9

Simplify the expression.

Rewrite using the commutative property of multiplication.

$2 y^{4} (2 x \sqrt{x})$

Multiply $2$ by $2$ .

$4 y^{4} x \sqrt{x}$

Simplify square root of 8xy^4* square root of 2x^2y^4

Related Questions

Support LCMGCF.com by disabling your adblocker.