Evaluate 8 square root of 54-4 square root of 6

$8 \sqrt{54} - 4 \sqrt{6}$

Step 1

Simplify each term.

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

Factor $9$ out of $54$ .

$8 \sqrt{9 (6)} - 4 \sqrt{6}$

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

$8 \sqrt{3^{2} \cdot 6} - 4 \sqrt{6}$

$8 \sqrt{3^{2} \cdot 6} - 4 \sqrt{6}$

Pull terms out from under the radical.

$8 (3 \sqrt{6}) - 4 \sqrt{6}$

Multiply $3$ by $8$ .

$24 \sqrt{6} - 4 \sqrt{6}$

$24 \sqrt{6} - 4 \sqrt{6}$

Step 2

Subtract $4 \sqrt{6}$ from $24 \sqrt{6}$ .

$20 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{6}$

Decimal Form:

$48.98979485 \dots$

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