Simplify square root of 135+5 square root of 10d-3 square root of 60

$\sqrt{135} + 5 \sqrt{10 d} - 3 \sqrt{60}$

Simplify each term.

Rewrite $135$ as $3^{2} \cdot 15$ .

Factor $9$ out of $135$ .

$\sqrt{9 (15)} + 5 \sqrt{10 d} - 3 \sqrt{60}$

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

$\sqrt{3^{2} \cdot 15} + 5 \sqrt{10 d} - 3 \sqrt{60}$

Pull terms out from under the radical.

$3 \sqrt{15} + 5 \sqrt{10 d} - 3 \sqrt{60}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$3 \sqrt{15} + 5 \sqrt{10 d} - 3 \sqrt{4 (15)}$

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

$3 \sqrt{15} + 5 \sqrt{10 d} - 3 \sqrt{2^{2} \cdot 15}$

Pull terms out from under the radical.

$3 \sqrt{15} + 5 \sqrt{10 d} - 3 (2 \sqrt{15})$

Multiply $2$ by $- 3$ .

$3 \sqrt{15} + 5 \sqrt{10 d} - 6 \sqrt{15}$

Subtract $6 \sqrt{15}$ from $3 \sqrt{15}$ .

$- 3 \sqrt{15} + 5 \sqrt{10 d}$