Simplify square root of 11y( square root of 11- square root of y)

$\sqrt{11 y} (\sqrt{11} - \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{11 y} \sqrt{11} + \sqrt{11 y} (- \sqrt{y})$

Step 2

Multiply $\sqrt{11 y} \sqrt{11}$ .

Combine using the product rule for radicals.

$\sqrt{11 y \cdot 11} + \sqrt{11 y} (- \sqrt{y})$

Multiply $11$ by $11$ .

$\sqrt{121 y} + \sqrt{11 y} (- \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{121 y} - \sqrt{11 y} \sqrt{y}$

Step 4

Simplify each term.

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2} y} - \sqrt{11 y} \sqrt{y}$

Pull terms out from under the radical.

$11 \sqrt{y} - \sqrt{11 y} \sqrt{y}$

Multiply $- \sqrt{11 y} \sqrt{y}$ .

Combine using the product rule for radicals.

$11 \sqrt{y} - \sqrt{y (11 y)}$

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

$11 \sqrt{y} - \sqrt{11 (y^{1} y)}$

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

$11 \sqrt{y} - \sqrt{11 (y^{1} y^{1})}$

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

$11 \sqrt{y} - \sqrt{11 y^{1 + 1}}$

Add $1$ and $1$ .

$11 \sqrt{y} - \sqrt{11 y^{2}}$

Reorder $11$ and $y^{2}$ .

$11 \sqrt{y} - \sqrt{y^{2} \cdot 11}$

Pull terms out from under the radical.

$11 \sqrt{y} - y \sqrt{11}$