Simplify square root of 2y( square root of 2- square root of y)

$\sqrt{2 y} (\sqrt{2} - \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{2 y} \sqrt{2} + \sqrt{2 y} (- \sqrt{y})$

Step 2

Multiply $\sqrt{2 y} \sqrt{2}$ .

Combine using the product rule for radicals.

$\sqrt{2 y \cdot 2} + \sqrt{2 y} (- \sqrt{y})$

Multiply $2$ by $2$ .

$\sqrt{4 y} + \sqrt{2 y} (- \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{4 y} - \sqrt{2 y} \sqrt{y}$

Step 4

Simplify each term.

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

$\sqrt{2^{2} y} - \sqrt{2 y} \sqrt{y}$

Pull terms out from under the radical.

$2 \sqrt{y} - \sqrt{2 y} \sqrt{y}$

Multiply $- \sqrt{2 y} \sqrt{y}$ .

Combine using the product rule for radicals.

$2 \sqrt{y} - \sqrt{y (2 y)}$

Raise $y$ to the power of $1$ .

$2 \sqrt{y} - \sqrt{2 (y^{1} y)}$

Raise $y$ to the power of $1$ .

$2 \sqrt{y} - \sqrt{2 (y^{1} y^{1})}$

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

$2 \sqrt{y} - \sqrt{2 y^{1 + 1}}$

Add $1$ and $1$ .

$2 \sqrt{y} - \sqrt{2 y^{2}}$

Reorder $2$ and $y^{2}$ .

$2 \sqrt{y} - \sqrt{y^{2} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt{y} - y \sqrt{2}$