Evaluate square root of 39( square root of 6+7)

$\sqrt{39} (\sqrt{6} + 7)$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt{39} \sqrt{6} + \sqrt{39} \cdot 7$

Combine using the product rule for radicals.

$\sqrt{39 \cdot 6} + \sqrt{39} \cdot 7$

Move $7$ to the left of $\sqrt{39}$ .

$\sqrt{39 \cdot 6} + 7 \cdot \sqrt{39}$

$\sqrt{39 \cdot 6} + 7 \cdot \sqrt{39}$

Step 2

Simplify each term.

Multiply $39$ by $6$ .

$\sqrt{234} + 7 \cdot \sqrt{39}$

Rewrite $234$ as $3^{2} \cdot 26$ .

Factor $9$ out of $234$ .

$\sqrt{9 (26)} + 7 \cdot \sqrt{39}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 26} + 7 \cdot \sqrt{39}$

$\sqrt{3^{2} \cdot 26} + 7 \cdot \sqrt{39}$

Pull terms out from under the radical.

$3 \sqrt{26} + 7 \sqrt{39}$

$3 \sqrt{26} + 7 \sqrt{39}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{26} + 7 \sqrt{39}$

Decimal Form:

$59.01204452 \dots$

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