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

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

Step 1

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} (- \sqrt{2})$

Step 2

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

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

${\sqrt{x}}^{1} \sqrt{x} + \sqrt{x} (- \sqrt{2})$

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

${\sqrt{x}}^{1} {\sqrt{x}}^{1} + \sqrt{x} (- \sqrt{2})$

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

${\sqrt{x}}^{1 + 1} + \sqrt{x} (- \sqrt{2})$

Add $1$ and $1$ .

${\sqrt{x}}^{2} + \sqrt{x} (- \sqrt{2})$

Step 3

Combine using the product rule for radicals.

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

Step 4

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Step 5

Reorder factors in $x - \sqrt{x \cdot 2}$ .

$x - \sqrt{2 x}$