Simplify square root of 10x( square root of 10- square root of x)

$\sqrt{10 x} (\sqrt{10} - \sqrt{x})$

Step 1

Apply the distributive property.

$\sqrt{10 x} \sqrt{10} + \sqrt{10 x} (- \sqrt{x})$

Step 2

Multiply $\sqrt{10 x} \sqrt{10}$ .

Combine using the product rule for radicals.

$\sqrt{10 x \cdot 10} + \sqrt{10 x} (- \sqrt{x})$

Multiply $10$ by $10$ .

$\sqrt{100 x} + \sqrt{10 x} (- \sqrt{x})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{100 x} - \sqrt{10 x} \sqrt{x}$

Step 4

Simplify each term.

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} x} - \sqrt{10 x} \sqrt{x}$

Pull terms out from under the radical.

$10 \sqrt{x} - \sqrt{10 x} \sqrt{x}$

Multiply $- \sqrt{10 x} \sqrt{x}$ .

Combine using the product rule for radicals.

$10 \sqrt{x} - \sqrt{x (10 x)}$

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

$10 \sqrt{x} - \sqrt{10 (x^{1} x)}$

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

$10 \sqrt{x} - \sqrt{10 (x^{1} x^{1})}$

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

$10 \sqrt{x} - \sqrt{10 x^{1 + 1}}$

Add $1$ and $1$ .

$10 \sqrt{x} - \sqrt{10 x^{2}}$

Reorder $10$ and $x^{2}$ .

$10 \sqrt{x} - \sqrt{x^{2} \cdot 10}$

Pull terms out from under the radical.

$10 \sqrt{x} - x \sqrt{10}$