Evaluate square root of 125- square root of 245

$\sqrt{125} - \sqrt{245}$

Step 1

Simplify each term.

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)} - \sqrt{245}$

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

$\sqrt{5^{2} \cdot 5} - \sqrt{245}$

$\sqrt{5^{2} \cdot 5} - \sqrt{245}$

Pull terms out from under the radical.

$5 \sqrt{5} - \sqrt{245}$

Rewrite $245$ as $7^{2} \cdot 5$ .

Factor $49$ out of $245$ .

$5 \sqrt{5} - \sqrt{49 (5)}$

Rewrite $49$ as $7^{2}$ .

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

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

Pull terms out from under the radical.

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

Multiply $7$ by $- 1$ .

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

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

Step 2

Subtract $7 \sqrt{5}$ from $5 \sqrt{5}$ .

$- 2 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{5}$

Decimal Form:

$- 4.47213595 \dots$

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