Simplify square root of 15*3 square root of 5

$\sqrt{15} \cdot 3 \sqrt{5}$

Step 1

Multiply $\sqrt{15} (3 \sqrt{5})$ .

Combine using the product rule for radicals.

$3 \sqrt{15 \cdot 5}$

Multiply $15$ by $5$ .

$3 \sqrt{75}$

$3 \sqrt{75}$

Step 2

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$3 \sqrt{25 (3)}$

Rewrite $25$ as $5^{2}$ .

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

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

Step 3

Pull terms out from under the radical.

$3 (5 \sqrt{3})$

Step 4

Multiply $5$ by $3$ .

$15 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{3}$

Decimal Form:

$25.98076211 \dots$

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