Evaluate 6 square root of 24-5 square root of 54

$6 \sqrt{24} - 5 \sqrt{54}$

Step 1

Simplify each term.

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$6 \sqrt{4 (6)} - 5 \sqrt{54}$

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

$6 \sqrt{2^{2} \cdot 6} - 5 \sqrt{54}$

$6 \sqrt{2^{2} \cdot 6} - 5 \sqrt{54}$

Pull terms out from under the radical.

$6 (2 \sqrt{6}) - 5 \sqrt{54}$

Multiply $2$ by $6$ .

$12 \sqrt{6} - 5 \sqrt{54}$

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

Factor $9$ out of $54$ .

$12 \sqrt{6} - 5 \sqrt{9 (6)}$

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

$12 \sqrt{6} - 5 \sqrt{3^{2} \cdot 6}$

$12 \sqrt{6} - 5 \sqrt{3^{2} \cdot 6}$

Pull terms out from under the radical.

$12 \sqrt{6} - 5 (3 \sqrt{6})$

Multiply $3$ by $- 5$ .

$12 \sqrt{6} - 15 \sqrt{6}$

$12 \sqrt{6} - 15 \sqrt{6}$

Step 2

Subtract $15 \sqrt{6}$ from $12 \sqrt{6}$ .

$- 3 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{6}$

Decimal Form:

$- 7.34846922 \dots$

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