Trigonometry Examples

$\sqrt{3} (\sqrt{10} - 1)$

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

$\sqrt{3} \sqrt{10} + \sqrt{3} \cdot - 1$

Step 1.2

Combine using the product rule for radicals.

$\sqrt{3 \cdot 10} + \sqrt{3} \cdot - 1$

Step 1.3

Move $- 1$ to the left of $\sqrt{3}$ .

$\sqrt{3 \cdot 10} - 1 \cdot \sqrt{3}$

$\sqrt{3 \cdot 10} - 1 \cdot \sqrt{3}$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $10$ .

$\sqrt{30} - 1 \cdot \sqrt{3}$

Step 2.2

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$\sqrt{30} - \sqrt{3}$

$\sqrt{30} - \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{30} - \sqrt{3}$

Decimal Form:

$3.74517476 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$