Evaluate 3 square root of 8- square root of 32+3 square root of 72- square root of 75

$3 \sqrt{8} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Step 1

Simplify each term.

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$3 \sqrt{4 (2)} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

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

$3 \sqrt{2^{2} \cdot 2} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Pull terms out from under the radical.

$3 (2 \sqrt{2}) - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Multiply $2$ by $3$ .

$6 \sqrt{2} - \sqrt{32} + 3 \sqrt{72} - \sqrt{75}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$6 \sqrt{2} - \sqrt{16 (2)} + 3 \sqrt{72} - \sqrt{75}$

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

$6 \sqrt{2} - \sqrt{4^{2} \cdot 2} + 3 \sqrt{72} - \sqrt{75}$

Pull terms out from under the radical.

$6 \sqrt{2} - (4 \sqrt{2}) + 3 \sqrt{72} - \sqrt{75}$

Multiply $4$ by $- 1$ .

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{72} - \sqrt{75}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{36 (2)} - \sqrt{75}$

Rewrite $36$ as $6^{2}$ .

$6 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{6^{2} \cdot 2} - \sqrt{75}$

Pull terms out from under the radical.

$6 \sqrt{2} - 4 \sqrt{2} + 3 (6 \sqrt{2}) - \sqrt{75}$

Multiply $6$ by $3$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{75}$

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

Factor $25$ out of $75$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{25 (3)}$

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

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - (5 \sqrt{3})$

Multiply $5$ by $- 1$ .

$6 \sqrt{2} - 4 \sqrt{2} + 18 \sqrt{2} - 5 \sqrt{3}$

Step 2

Simplify by adding terms.

Subtract $4 \sqrt{2}$ from $6 \sqrt{2}$ .

$2 \sqrt{2} + 18 \sqrt{2} - 5 \sqrt{3}$

Add $2 \sqrt{2}$ and $18 \sqrt{2}$ .

$20 \sqrt{2} - 5 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{2} - 5 \sqrt{3}$

Decimal Form:

$19.62401720 \dots$

Evaluate 3 square root of 8- square root of 32+3 square root of 72- square root of 75

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