Simplify square root of 14y( square root of 14- square root of y)

$\sqrt{14 y} (\sqrt{14} - \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{14 y} \sqrt{14} + \sqrt{14 y} (- \sqrt{y})$

Step 2

Multiply $\sqrt{14 y} \sqrt{14}$ .

Combine using the product rule for radicals.

$\sqrt{14 y \cdot 14} + \sqrt{14 y} (- \sqrt{y})$

Multiply $14$ by $14$ .

$\sqrt{196 y} + \sqrt{14 y} (- \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{196 y} - \sqrt{14 y} \sqrt{y}$

Step 4

Simplify each term.

Rewrite $196$ as $14^{2}$ .

$\sqrt{14^{2} y} - \sqrt{14 y} \sqrt{y}$

Pull terms out from under the radical.

$14 \sqrt{y} - \sqrt{14 y} \sqrt{y}$

Multiply $- \sqrt{14 y} \sqrt{y}$ .

Combine using the product rule for radicals.

$14 \sqrt{y} - \sqrt{y (14 y)}$

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

$14 \sqrt{y} - \sqrt{14 (y^{1} y)}$

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

$14 \sqrt{y} - \sqrt{14 (y^{1} y^{1})}$

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

$14 \sqrt{y} - \sqrt{14 y^{1 + 1}}$

Add $1$ and $1$ .

$14 \sqrt{y} - \sqrt{14 y^{2}}$

Reorder $14$ and $y^{2}$ .

$14 \sqrt{y} - \sqrt{y^{2} \cdot 14}$

Pull terms out from under the radical.

$14 \sqrt{y} - y \sqrt{14}$