Basic Math Examples

$(\sqrt{7 + 3}) (\sqrt{14} - 3)$

Step 1

Simplify terms.

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Step 1.1

Add $7$ and $3$ .

$\sqrt{10} (\sqrt{14} - 3)$

Step 1.2

Apply the distributive property.

$\sqrt{10} \sqrt{14} + \sqrt{10} \cdot - 3$

Step 1.3

Combine using the product rule for radicals.

$\sqrt{10 \cdot 14} + \sqrt{10} \cdot - 3$

Step 1.4

Move $- 3$ to the left of $\sqrt{10}$ .

$\sqrt{10 \cdot 14} - 3 \cdot \sqrt{10}$

$\sqrt{10 \cdot 14} - 3 \cdot \sqrt{10}$

Step 2

Simplify each term.

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Step 2.1

Multiply $10$ by $14$ .

$\sqrt{140} - 3 \cdot \sqrt{10}$

Step 2.2

Rewrite $140$ as $2^{2} \cdot 35$ .

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Step 2.2.1

Factor $4$ out of $140$ .

$\sqrt{4 (35)} - 3 \cdot \sqrt{10}$

Step 2.2.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 35} - 3 \cdot \sqrt{10}$

$\sqrt{2^{2} \cdot 35} - 3 \cdot \sqrt{10}$

Step 2.3

Pull terms out from under the radical.

$2 \sqrt{35} - 3 \sqrt{10}$

$2 \sqrt{35} - 3 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{35} - 3 \sqrt{10}$

Decimal Form:

$2.34532658 \dots$

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