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

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

Step 1

Apply the distributive property.

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

Step 2

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

Combine using the product rule for radicals.

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

Multiply $14$ by $14$ .

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Simplify each term.

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

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

Pull terms out from under the radical.

$14 \sqrt{x} - \sqrt{14 x} \sqrt{x}$

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

Combine using the product rule for radicals.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Pull terms out from under the radical.

$14 \sqrt{x} - x \sqrt{14}$