Solve sqrt{{[(6:3+14+5):3+21:3]*5+23*6}:13}*sqrt{16}=

$$\sqrt { \{ [ ( 6 : 3 + 14 + 5 ) : 3 + 21 : 3 ] \cdot 5 + 23 \cdot 6 \} : 13 } \cdot \sqrt { 16 } =$$

Evaluate

$$16$$

Solution Steps

Divide 6 by 3 to get 2.

$$\sqrt{\frac{\left(\frac{2+14+5}{3}+\frac{21}{3}\right)\times 5+23\times 6}{13}}\sqrt{16}$$

Add 2 and 14 to get 16.

$$\sqrt{\frac{\left(\frac{16+5}{3}+\frac{21}{3}\right)\times 5+23\times 6}{13}}\sqrt{16}$$

Add 16 and 5 to get 21.

$$\sqrt{\frac{\left(\frac{21}{3}+\frac{21}{3}\right)\times 5+23\times 6}{13}}\sqrt{16}$$

Divide 21 by 3 to get 7.

$$\sqrt{\frac{\left(7+\frac{21}{3}\right)\times 5+23\times 6}{13}}\sqrt{16}$$

Divide 21 by 3 to get 7.

$$\sqrt{\frac{\left(7+7\right)\times 5+23\times 6}{13}}\sqrt{16}$$

Add 7 and 7 to get 14.

$$\sqrt{\frac{14\times 5+23\times 6}{13}}\sqrt{16}$$

Multiply 14 and 5 to get 70.

$$\sqrt{\frac{70+23\times 6}{13}}\sqrt{16}$$

Multiply 23 and 6 to get 138.

$$\sqrt{\frac{70+138}{13}}\sqrt{16}$$

Add 70 and 138 to get 208.

$$\sqrt{\frac{208}{13}}\sqrt{16}$$

Divide 208 by 13 to get 16.

$$\sqrt{16}\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4\times 4$$

Multiply 4 and 4 to get 16.

$$16$$

Factor

$$2^{4}$$