Simplify square root of 6y( square root of 6- square root of y)

$\sqrt{6 y} (\sqrt{6} - \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{6 y} \sqrt{6} + \sqrt{6 y} (- \sqrt{y})$

Step 2

Multiply $\sqrt{6 y} \sqrt{6}$ .

Combine using the product rule for radicals.

$\sqrt{6 y \cdot 6} + \sqrt{6 y} (- \sqrt{y})$

Multiply $6$ by $6$ .

$\sqrt{36 y} + \sqrt{6 y} (- \sqrt{y})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{36 y} - \sqrt{6 y} \sqrt{y}$

Step 4

Simplify each term.

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} y} - \sqrt{6 y} \sqrt{y}$

Pull terms out from under the radical.

$6 \sqrt{y} - \sqrt{6 y} \sqrt{y}$

Multiply $- \sqrt{6 y} \sqrt{y}$ .

Combine using the product rule for radicals.

$6 \sqrt{y} - \sqrt{y (6 y)}$

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

$6 \sqrt{y} - \sqrt{6 (y^{1} y)}$

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

$6 \sqrt{y} - \sqrt{6 (y^{1} y^{1})}$

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

$6 \sqrt{y} - \sqrt{6 y^{1 + 1}}$

Add $1$ and $1$ .

$6 \sqrt{y} - \sqrt{6 y^{2}}$

Reorder $6$ and $y^{2}$ .

$6 \sqrt{y} - \sqrt{y^{2} \cdot 6}$

Pull terms out from under the radical.

$6 \sqrt{y} - y \sqrt{6}$