Simplify 5^3 square root of 16-3^3 square root of 54

$5^{3} \sqrt{16} - 3^{3} \sqrt{54}$

Step 1

Raise $5$ to the power of $3$ .

$125 \sqrt{16} - 3^{3} \sqrt{54}$

Step 2

Rewrite $16$ as $4^{2}$ .

$125 \sqrt{4^{2}} - 3^{3} \sqrt{54}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$125 \cdot 4 - 3^{3} \sqrt{54}$

Step 4

Multiply $125$ by $4$ .

$500 - 3^{3} \sqrt{54}$

Step 5

Raise $3$ to the power of $3$ .

$500 - 1 \cdot 27 \sqrt{54}$

Step 6

Multiply $- 1$ by $27$ .

$500 - 27 \sqrt{54}$

Step 7

Rewrite $54$ as $3^{2} \cdot 6$ .

Factor $9$ out of $54$ .

$500 - 27 \sqrt{9 (6)}$

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

$500 - 27 \sqrt{3^{2} \cdot 6}$

Step 8

Pull terms out from under the radical.

$500 - 27 (3 \sqrt{6})$

Step 9

Multiply $3$ by $- 27$ .

$500 - 81 \sqrt{6}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$500 - 81 \sqrt{6}$

Decimal Form:

$301.59133083 \dots$