Simplify square root of 10y( square root of 10- square root of y)

$\sqrt{10 y} (\sqrt{10} - \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{10 y} \sqrt{10} + \sqrt{10 y} (- \sqrt{y})$

Step 2

Multiply $\sqrt{10 y} \sqrt{10}$ .

Combine using the product rule for radicals.

$\sqrt{10 y \cdot 10} + \sqrt{10 y} (- \sqrt{y})$

Multiply $10$ by $10$ .

$\sqrt{100 y} + \sqrt{10 y} (- \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{100 y} - \sqrt{10 y} \sqrt{y}$

Step 4

Simplify each term.

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} y} - \sqrt{10 y} \sqrt{y}$

Pull terms out from under the radical.

$10 \sqrt{y} - \sqrt{10 y} \sqrt{y}$

Multiply $- \sqrt{10 y} \sqrt{y}$ .

Combine using the product rule for radicals.

$10 \sqrt{y} - \sqrt{y (10 y)}$

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

$10 \sqrt{y} - \sqrt{10 (y^{1} y)}$

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

$10 \sqrt{y} - \sqrt{10 (y^{1} y^{1})}$

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

$10 \sqrt{y} - \sqrt{10 y^{1 + 1}}$

Add $1$ and $1$ .

$10 \sqrt{y} - \sqrt{10 y^{2}}$

Reorder $10$ and $y^{2}$ .

$10 \sqrt{y} - \sqrt{y^{2} \cdot 10}$

Pull terms out from under the radical.

$10 \sqrt{y} - y \sqrt{10}$