Simplify 5 square root of 75

$5 \sqrt{75}$

Step 1

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$5 \sqrt{25 (3)}$

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

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

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

Step 2

Pull terms out from under the radical.

$5 (5 \sqrt{3})$

Step 3

Multiply $5$ by $5$ .

$25 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$25 \sqrt{3}$

Decimal Form:

$43.30127018 \dots$

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