Simplify square root of 13x( square root of 13- square root of x)

$\sqrt{13 x} (\sqrt{13} - \sqrt{x})$

Step 1

Apply the distributive property.

$\sqrt{13 x} \sqrt{13} + \sqrt{13 x} (- \sqrt{x})$

Step 2

Multiply $\sqrt{13 x} \sqrt{13}$ .

Combine using the product rule for radicals.

$\sqrt{13 x \cdot 13} + \sqrt{13 x} (- \sqrt{x})$

Multiply $13$ by $13$ .

$\sqrt{169 x} + \sqrt{13 x} (- \sqrt{x})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{169 x} - \sqrt{13 x} \sqrt{x}$

Step 4

Simplify each term.

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2} x} - \sqrt{13 x} \sqrt{x}$

Pull terms out from under the radical.

$13 \sqrt{x} - \sqrt{13 x} \sqrt{x}$

Multiply $- \sqrt{13 x} \sqrt{x}$ .

Combine using the product rule for radicals.

$13 \sqrt{x} - \sqrt{x (13 x)}$

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

$13 \sqrt{x} - \sqrt{13 (x^{1} x)}$

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

$13 \sqrt{x} - \sqrt{13 (x^{1} x^{1})}$

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

$13 \sqrt{x} - \sqrt{13 x^{1 + 1}}$

Add $1$ and $1$ .

$13 \sqrt{x} - \sqrt{13 x^{2}}$

Reorder $13$ and $x^{2}$ .

$13 \sqrt{x} - \sqrt{x^{2} \cdot 13}$

Pull terms out from under the radical.

$13 \sqrt{x} - x \sqrt{13}$