Solve sqrt{9*sqrt{16}}-sqrt{5*sqrt{25}}+sqrt{8*sqrt{4}}

$$\sqrt { 9 \cdot \sqrt { 16 } } - \sqrt { 5 \cdot \sqrt { 25 } } + \sqrt { 8 \cdot \sqrt { 4 } }$$

Evaluate

$$5$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\sqrt{9\times 4}-\sqrt{5\sqrt{25}}+\sqrt{8\sqrt{4}}$$

Multiply 9 and 4 to get 36.

$$\sqrt{36}-\sqrt{5\sqrt{25}}+\sqrt{8\sqrt{4}}$$

Calculate the square root of 36 and get 6.

$$6-\sqrt{5\sqrt{25}}+\sqrt{8\sqrt{4}}$$

Calculate the square root of 25 and get 5.

$$6-\sqrt{5\times 5}+\sqrt{8\sqrt{4}}$$

Multiply 5 and 5 to get 25.

$$6-\sqrt{25}+\sqrt{8\sqrt{4}}$$

Calculate the square root of 25 and get 5.

$$6-5+\sqrt{8\sqrt{4}}$$

Subtract 5 from 6 to get 1.

$$1+\sqrt{8\sqrt{4}}$$

Calculate the square root of 4 and get 2.

$$1+\sqrt{8\times 2}$$

Multiply 8 and 2 to get 16.

$$1+\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$1+4$$

Add 1 and 4 to get 5.

$$5$$

Factor

$$5$$