Algebra Examples

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

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Combine using the product rule for radicals.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

Add $1$ and $1$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

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

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

Step 2.2.4

Cancel the common factor of $2$ .

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Step 2.2.4.1

Cancel the common factor.

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

Step 2.2.4.2

Rewrite the expression.

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

Step 2.2.5

Simplify.

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

Step 3

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

$\sqrt{5 x} - x$