Simplify 14 square root of 20-3 square root of 125

$14 \sqrt{20} - 3 \sqrt{125}$

Step 1

Simplify each term.

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$14 \sqrt{4 (5)} - 3 \sqrt{125}$

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

$14 \sqrt{2^{2} \cdot 5} - 3 \sqrt{125}$

$14 \sqrt{2^{2} \cdot 5} - 3 \sqrt{125}$

Pull terms out from under the radical.

$14 (2 \sqrt{5}) - 3 \sqrt{125}$

Multiply $2$ by $14$ .

$28 \sqrt{5} - 3 \sqrt{125}$

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

Factor $25$ out of $125$ .

$28 \sqrt{5} - 3 \sqrt{25 (5)}$

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

$28 \sqrt{5} - 3 \sqrt{5^{2} \cdot 5}$

$28 \sqrt{5} - 3 \sqrt{5^{2} \cdot 5}$

Pull terms out from under the radical.

$28 \sqrt{5} - 3 (5 \sqrt{5})$

Multiply $5$ by $- 3$ .

$28 \sqrt{5} - 15 \sqrt{5}$

$28 \sqrt{5} - 15 \sqrt{5}$

Step 2

Subtract $15 \sqrt{5}$ from $28 \sqrt{5}$ .

$13 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$13 \sqrt{5}$

Decimal Form:

$29.06888370 \dots$

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