Solve sqrt{12}*sqrt{3}*5+sqrt{25}*(sqrt{16}+5)]:3-sqrt{32}*sqrt{2}*sqrt{9}

$$\sqrt { 12 } \times \sqrt { 3 } \times 5 + \sqrt { 25 } \times ( \sqrt { 16 } + 5 ) ] : 3 - \sqrt { 32 } \times \sqrt { 2 } \times \sqrt { 9 }$$

Evaluate

$$75$$

Solution Steps

Factor 12=3\times 4. Rewrite the square root of the product \sqrt{3\times 4} as the product of square roots \sqrt{3}\sqrt{4}.

$$5\sqrt{3}\sqrt{4}\sqrt{3}+\sqrt{25}\left(\sqrt{16}+5\right)$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$5\times 3\sqrt{4}+\sqrt{25}\left(\sqrt{16}+5\right)$$

Multiply 5 and 3 to get 15.

$$15\sqrt{4}+\sqrt{25}\left(\sqrt{16}+5\right)$$

Calculate the square root of 4 and get 2.

$$15\times 2+\sqrt{25}\left(\sqrt{16}+5\right)$$

Multiply 15 and 2 to get 30.

$$30+\sqrt{25}\left(\sqrt{16}+5\right)$$

Calculate the square root of 25 and get 5.

$$30+5\left(\sqrt{16}+5\right)$$

Calculate the square root of 16 and get 4.

$$30+5\left(4+5\right)$$

Add 4 and 5 to get 9.

$$30+5\times 9$$

Multiply 5 and 9 to get 45.

$$30+45$$

Add 30 and 45 to get 75.

$$75$$

Factor

$$3\times 5^{2}$$