Simplify square root of 11(4 square root of 7- square root of 175)

$\sqrt{11} (4 \sqrt{7} - \sqrt{175})$

Step 1

Simplify each term.

Rewrite $175$ as $5^{2} \cdot 7$ .

Factor $25$ out of $175$ .

$\sqrt{11} (4 \sqrt{7} - \sqrt{25 (7)})$

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

$\sqrt{11} (4 \sqrt{7} - \sqrt{5^{2} \cdot 7})$

$\sqrt{11} (4 \sqrt{7} - \sqrt{5^{2} \cdot 7})$

Pull terms out from under the radical.

$\sqrt{11} (4 \sqrt{7} - (5 \sqrt{7}))$

Multiply $5$ by $- 1$ .

$\sqrt{11} (4 \sqrt{7} - 5 \sqrt{7})$

$\sqrt{11} (4 \sqrt{7} - 5 \sqrt{7})$

Step 2

Subtract $5 \sqrt{7}$ from $4 \sqrt{7}$ .

$\sqrt{11} (- \sqrt{7})$

Step 3

Multiply $\sqrt{11} (- \sqrt{7})$ .

Combine using the product rule for radicals.

$- \sqrt{11 \cdot 7}$

Multiply $11$ by $7$ .

$- \sqrt{77}$

$- \sqrt{77}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{77}$

Decimal Form:

$- 8.77496438 \dots$

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