Finite Math Examples

$\sqrt{15 (3 \sqrt{6 + 2 \sqrt{5}})}$

Step 1

Multiply $15$ by $3$ .

$\sqrt{45 \sqrt{6 + 2 \sqrt{5}}}$

Step 2

Rewrite $45 \sqrt{6 + 2 \sqrt{5}}$ as $3^{2} \cdot (5 \sqrt{6 + 2 \sqrt{5}})$ .

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Step 2.1

Factor $9$ out of $45$ .

$\sqrt{9 (5) \sqrt{6 + 2 \sqrt{5}}}$

Step 2.2

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

$\sqrt{3^{2} \cdot 5 \sqrt{6 + 2 \sqrt{5}}}$

Step 2.3

Add parentheses.

$\sqrt{3^{2} \cdot (5 \sqrt{6 + 2 \sqrt{5}})}$

Step 3

Pull terms out from under the radical.

$3 \sqrt{5 \sqrt{6 + 2 \sqrt{5}}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5 \sqrt{6 + 2 \sqrt{5}}}$

Decimal Form:

$12.06743796 \dots$