Simplify (3/4* square root of 15)(16 square root of 5)

$(\frac{3}{4} \cdot \sqrt{15}) (16 \sqrt{5})$

Step 1

Combine $\frac{3}{4}$ and $\sqrt{15}$ .

$\frac{3 \sqrt{15}}{4} (16 \sqrt{5})$

Step 2

Cancel the common factor of $4$ .

Factor $4$ out of $16 \sqrt{5}$ .

$\frac{3 \sqrt{15}}{4} (4 (4 \sqrt{5}))$

Cancel the common factor.

$\frac{3 \sqrt{15}}{4} (4 (4 \sqrt{5}))$

Rewrite the expression.

$3 \sqrt{15} (4 \sqrt{5})$

$3 \sqrt{15} (4 \sqrt{5})$

Step 3

Multiply $4$ by $3$ .

$12 \sqrt{15} \sqrt{5}$

Step 4

Combine using the product rule for radicals.

$12 \sqrt{5 \cdot 15}$

Step 5

Multiply $5$ by $15$ .

$12 \sqrt{75}$

Step 6

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

Factor $25$ out of $75$ .

$12 \sqrt{25 (3)}$

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

$12 \sqrt{5^{2} \cdot 3}$

$12 \sqrt{5^{2} \cdot 3}$

Step 7

Pull terms out from under the radical.

$12 (5 \sqrt{3})$

Step 8

Multiply $5$ by $12$ .

$60 \sqrt{3}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$60 \sqrt{3}$

Decimal Form:

$103.92304845 \dots$

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