Simplify square root of 7(2 square root of 5- square root of 125)

$\sqrt{7} (2 \sqrt{5} - \sqrt{125})$

Step 1

Simplify each term.

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

Factor $25$ out of $125$ .

$\sqrt{7} (2 \sqrt{5} - \sqrt{25 (5)})$

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

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

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

Pull terms out from under the radical.

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

Multiply $5$ by $- 1$ .

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

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

Step 2

Subtract $5 \sqrt{5}$ from $2 \sqrt{5}$ .

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

Step 3

Multiply $\sqrt{7} (- 3 \sqrt{5})$ .

Combine using the product rule for radicals.

$- 3 \sqrt{7 \cdot 5}$

Multiply $7$ by $5$ .

$- 3 \sqrt{35}$

$- 3 \sqrt{35}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- 3 \sqrt{35}$

Decimal Form:

$- 17.74823934 \dots$

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