Evaluate 3 square root of 12+7 square root of 75- square root of 54

$3 \sqrt{12} + 7 \sqrt{75} - \sqrt{54}$

Step 1

Simplify each term.

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$3 \sqrt{4 (3)} + 7 \sqrt{75} - \sqrt{54}$

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

$3 \sqrt{2^{2} \cdot 3} + 7 \sqrt{75} - \sqrt{54}$

$3 \sqrt{2^{2} \cdot 3} + 7 \sqrt{75} - \sqrt{54}$

Pull terms out from under the radical.

$3 (2 \sqrt{3}) + 7 \sqrt{75} - \sqrt{54}$

Multiply $2$ by $3$ .

$6 \sqrt{3} + 7 \sqrt{75} - \sqrt{54}$

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

Factor $25$ out of $75$ .

$6 \sqrt{3} + 7 \sqrt{25 (3)} - \sqrt{54}$

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

$6 \sqrt{3} + 7 \sqrt{5^{2} \cdot 3} - \sqrt{54}$

$6 \sqrt{3} + 7 \sqrt{5^{2} \cdot 3} - \sqrt{54}$

Pull terms out from under the radical.

$6 \sqrt{3} + 7 (5 \sqrt{3}) - \sqrt{54}$

Multiply $5$ by $7$ .

$6 \sqrt{3} + 35 \sqrt{3} - \sqrt{54}$

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

Factor $9$ out of $54$ .

$6 \sqrt{3} + 35 \sqrt{3} - \sqrt{9 (6)}$

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

$6 \sqrt{3} + 35 \sqrt{3} - \sqrt{3^{2} \cdot 6}$

$6 \sqrt{3} + 35 \sqrt{3} - \sqrt{3^{2} \cdot 6}$

Pull terms out from under the radical.

$6 \sqrt{3} + 35 \sqrt{3} - (3 \sqrt{6})$

Multiply $3$ by $- 1$ .

$6 \sqrt{3} + 35 \sqrt{3} - 3 \sqrt{6}$

$6 \sqrt{3} + 35 \sqrt{3} - 3 \sqrt{6}$

Step 2

Add $6 \sqrt{3}$ and $35 \sqrt{3}$ .

$41 \sqrt{3} - 3 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$41 \sqrt{3} - 3 \sqrt{6}$

Decimal Form:

$63.66561388 \dots$

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