Evaluate 11 square root of 45-4 square root of 5

$11 \sqrt{45} - 4 \sqrt{5}$

Step 1

Simplify each term.

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$11 \sqrt{9 (5)} - 4 \sqrt{5}$

Rewrite $9$ as $3^{2}$ .

$11 \sqrt{3^{2} \cdot 5} - 4 \sqrt{5}$

$11 \sqrt{3^{2} \cdot 5} - 4 \sqrt{5}$

Pull terms out from under the radical.

$11 (3 \sqrt{5}) - 4 \sqrt{5}$

Multiply $3$ by $11$ .

$33 \sqrt{5} - 4 \sqrt{5}$

$33 \sqrt{5} - 4 \sqrt{5}$

Step 2

Subtract $4 \sqrt{5}$ from $33 \sqrt{5}$ .

$29 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$29 \sqrt{5}$

Decimal Form:

$64.84597134 \dots$

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