Simplify square root of x( square root of 5- square root of x)

$\sqrt{x} (\sqrt{5} - \sqrt{x})$

Simplify terms.

Apply the distributive property.

$\sqrt{x} \sqrt{5} + \sqrt{x} (- \sqrt{x})$

Combine using the product rule for radicals.

$\sqrt{x \cdot 5} + \sqrt{x} (- \sqrt{x})$

Rewrite using the commutative property of multiplication.

$\sqrt{x \cdot 5} - \sqrt{x} \sqrt{x}$

Simplify each term.

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

Raise $\sqrt{x}$ to the power of $1$ .

$\sqrt{x \cdot 5} - ({\sqrt{x}}^{1} \sqrt{x})$

Raise $\sqrt{x}$ to the power of $1$ .

$\sqrt{x \cdot 5} - ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$\sqrt{x \cdot 5} - {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$\sqrt{x \cdot 5} - {\sqrt{x}}^{2}$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\sqrt{x \cdot 5} - {(x^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\sqrt{x \cdot 5} - x^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$\sqrt{x \cdot 5} - x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\sqrt{x \cdot 5} - x^{\frac{2}{2}}$

Rewrite the expression.

$\sqrt{x \cdot 5} - x^{1}$

Simplify.

$\sqrt{x \cdot 5} - x$

Reorder factors in $\sqrt{x \cdot 5} - x$ .

$\sqrt{5 x} - x$