Multiply 9 square root of 5( square root of 15- square root of 6)

$9 \sqrt{5} (\sqrt{15} - \sqrt{6})$

Apply the distributive property.

$9 \sqrt{5} \sqrt{15} + 9 \sqrt{5} (- \sqrt{6})$

Multiply $9 \sqrt{5} \sqrt{15}$ .

Tap for more steps…

Combine using the product rule for radicals.

$9 \sqrt{15 \cdot 5} + 9 \sqrt{5} (- \sqrt{6})$

Multiply $15$ by $5$ .

$9 \sqrt{75} + 9 \sqrt{5} (- \sqrt{6})$

Multiply $9 \sqrt{5} (- \sqrt{6})$ .

Tap for more steps…

Multiply $- 1$ by $9$ .

$9 \sqrt{75} - 9 \sqrt{5} \sqrt{6}$

Combine using the product rule for radicals.

$9 \sqrt{75} - 9 \sqrt{6 \cdot 5}$

Multiply $6$ by $5$ .

$9 \sqrt{75} - 9 \sqrt{30}$

Simplify each term.

Tap for more steps…

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

Tap for more steps…

Factor $25$ out of $75$ .

$9 \sqrt{25 (3)} - 9 \sqrt{30}$

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

$9 \sqrt{5^{2} \cdot 3} - 9 \sqrt{30}$

Pull terms out from under the radical.

$9 (5 \sqrt{3}) - 9 \sqrt{30}$

Multiply $5$ by $9$ .

$45 \sqrt{3} - 9 \sqrt{30}$

The result can be shown in multiple forms.

Exact Form:

$45 \sqrt{3} - 9 \sqrt{30}$

Decimal Form:

$28.64725616 \dots$

Multiply 9 square root of 5( square root of 15- square root of 6)