Solve (5-3)^4div4{sqrt{6^2-20}+sqrt{5*4+16}+(8-4)^2*3}

$$( 5 - 3 ) ^ { 4 } \div 4 \{ \sqrt { 6 ^ { 2 } - 20 } + \sqrt { 5 \times 4 + 16 } + ( 8 - 4 ) ^ { 2 } \times 3 \}$$

Evaluate

$$232$$

Solution Steps

Subtract 3 from 5 to get 2.

$$\frac{2^{4}}{4}\left(\sqrt{6^{2}-20}+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16}{4}\left(\sqrt{6^{2}-20}+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Divide 16 by 4 to get 4.

$$4\left(\sqrt{6^{2}-20}+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Calculate 6 to the power of 2 and get 36.

$$4\left(\sqrt{36-20}+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Subtract 20 from 36 to get 16.

$$4\left(\sqrt{16}+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Calculate the square root of 16 and get 4.

$$4\left(4+\sqrt{5\times 4+16}+\left(8-4\right)^{2}\times 3\right)$$

Multiply 5 and 4 to get 20.

$$4\left(4+\sqrt{20+16}+\left(8-4\right)^{2}\times 3\right)$$

Add 20 and 16 to get 36.

$$4\left(4+\sqrt{36}+\left(8-4\right)^{2}\times 3\right)$$

Calculate the square root of 36 and get 6.

$$4\left(4+6+\left(8-4\right)^{2}\times 3\right)$$

Add 4 and 6 to get 10.

$$4\left(10+\left(8-4\right)^{2}\times 3\right)$$

Subtract 4 from 8 to get 4.

$$4\left(10+4^{2}\times 3\right)$$

Calculate 4 to the power of 2 and get 16.

$$4\left(10+16\times 3\right)$$

Multiply 16 and 3 to get 48.

$$4\left(10+48\right)$$

Add 10 and 48 to get 58.

$$4\times 58$$

Multiply 4 and 58 to get 232.

$$232$$

Factor

$$2^{3}\times 29$$