Evaluate (6 square root of 5- square root of 125)* square root of 45

$(6 \sqrt{5} - \sqrt{125}) \cdot \sqrt{45}$

Step 1

Simplify each term.

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

Factor $25$ out of $125$ .

$(6 \sqrt{5} - \sqrt{25 (5)}) \cdot \sqrt{45}$

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

$(6 \sqrt{5} - \sqrt{5^{2} \cdot 5}) \cdot \sqrt{45}$

Pull terms out from under the radical.

$(6 \sqrt{5} - (5 \sqrt{5})) \cdot \sqrt{45}$

Multiply $5$ by $- 1$ .

$(6 \sqrt{5} - 5 \sqrt{5}) \cdot \sqrt{45}$

Step 2

Simplify terms.

Subtract $5 \sqrt{5}$ from $6 \sqrt{5}$ .

$\sqrt{5} \cdot \sqrt{45}$

Combine using the product rule for radicals.

$\sqrt{5 \cdot 45}$

Write the expression using exponents.

Multiply $5$ by $45$ .

$\sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$15$