Simplify square root of 14x(3- square root of 2x)

$\sqrt{14 x} (3 - \sqrt{2 x})$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$\sqrt{14 x} \cdot 3 + \sqrt{14 x} (- \sqrt{2 x})$

Reorder.

Move $3$ to the left of $\sqrt{14 x}$ .

$3 \cdot \sqrt{14 x} + \sqrt{14 x} (- \sqrt{2 x})$

Rewrite using the commutative property of multiplication.

$3 \cdot \sqrt{14 x} - \sqrt{14 x} \sqrt{2 x}$

Step 2

Simplify each term.

Multiply $- \sqrt{14 x} \sqrt{2 x}$ .

Combine using the product rule for radicals.

$3 \sqrt{14 x} - \sqrt{2 x (14 x)}$

Multiply $14$ by $2$ .

$3 \sqrt{14 x} - \sqrt{28 x \cdot x}$

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

$3 \sqrt{14 x} - \sqrt{28 (x^{1} x)}$

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

$3 \sqrt{14 x} - \sqrt{28 (x^{1} x^{1})}$

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

$3 \sqrt{14 x} - \sqrt{28 x^{1 + 1}}$

Add $1$ and $1$ .

$3 \sqrt{14 x} - \sqrt{28 x^{2}}$

Rewrite $28 x^{2}$ as ${(2 x)}^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$3 \sqrt{14 x} - \sqrt{4 (7) x^{2}}$

Rewrite $4$ as $2^{2}$ .

$3 \sqrt{14 x} - \sqrt{2^{2} \cdot 7 x^{2}}$

Move $7$ .

$3 \sqrt{14 x} - \sqrt{2^{2} x^{2} \cdot 7}$

Rewrite $2^{2} x^{2}$ as ${(2 x)}^{2}$ .

$3 \sqrt{14 x} - \sqrt{{(2 x)}^{2} \cdot 7}$

Pull terms out from under the radical.

$3 \sqrt{14 x} - (2 x \sqrt{7})$

Multiply $2$ by $- 1$ .

$3 \sqrt{14 x} - 2 x \sqrt{7}$