Evaluate 2 square root of 28-5 square root of 63

$2 \sqrt{28} - 5 \sqrt{63}$

Step 1

Simplify each term.

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$2 \sqrt{4 (7)} - 5 \sqrt{63}$

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

$2 \sqrt{2^{2} \cdot 7} - 5 \sqrt{63}$

$2 \sqrt{2^{2} \cdot 7} - 5 \sqrt{63}$

Pull terms out from under the radical.

$2 (2 \sqrt{7}) - 5 \sqrt{63}$

Multiply $2$ by $2$ .

$4 \sqrt{7} - 5 \sqrt{63}$

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$4 \sqrt{7} - 5 \sqrt{9 (7)}$

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

$4 \sqrt{7} - 5 \sqrt{3^{2} \cdot 7}$

$4 \sqrt{7} - 5 \sqrt{3^{2} \cdot 7}$

Pull terms out from under the radical.

$4 \sqrt{7} - 5 (3 \sqrt{7})$

Multiply $3$ by $- 5$ .

$4 \sqrt{7} - 15 \sqrt{7}$

$4 \sqrt{7} - 15 \sqrt{7}$

Step 2

Subtract $15 \sqrt{7}$ from $4 \sqrt{7}$ .

$- 11 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 11 \sqrt{7}$

Decimal Form:

$- 29.10326442 \dots$

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