Solve sqrt{361}-(sqrt{36}-sqrt{16})*(10+(sqrt{25}-6)+[11-(2*sqrt{9}+7-sqrt{3}*3+27)*4]-14)=

$$\sqrt { 361 } - ( \sqrt { 36 } - \sqrt { 16 } ) \cdot ( 10 + ( \sqrt { 25 } - 6 ) + [ 11 - ( 2 \cdot \sqrt { 9 } + 7 - \sqrt { 3 } \cdot 3 + 27 ) \cdot 4 ] - 14 ) =$$

Evaluate

$$327-24\sqrt{3}\approx 285.430780618$$

Solution Steps

Calculate the square root of 361 and get 19.

$$19-\left(\sqrt{36}-\sqrt{16}\right)\left(10+\sqrt{25}-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Calculate the square root of 36 and get 6.

$$19-\left(6-\sqrt{16}\right)\left(10+\sqrt{25}-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Calculate the square root of 16 and get 4.

$$19-\left(6-4\right)\left(10+\sqrt{25}-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Subtract 4 from 6 to get 2.

$$19-2\left(10+\sqrt{25}-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Calculate the square root of 25 and get 5.

$$19-2\left(10+5-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Add 10 and 5 to get 15.

$$19-2\left(15-6+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Subtract 6 from 15 to get 9.

$$19-2\left(9+11-4\left(2\sqrt{9}+7-3\sqrt{3}+27\right)-14\right)$$

Calculate the square root of 9 and get 3.

$$19-2\left(9+11-4\left(2\times 3+7-3\sqrt{3}+27\right)-14\right)$$

Multiply 2 and 3 to get 6.

$$19-2\left(9+11-4\left(6+7-3\sqrt{3}+27\right)-14\right)$$

Add 6 and 7 to get 13.

$$19-2\left(9+11-4\left(13-3\sqrt{3}+27\right)-14\right)$$

Add 13 and 27 to get 40.

$$19-2\left(9+11-4\left(40-3\sqrt{3}\right)-14\right)$$

Subtract 14 from 9 to get -5.

$$19-2\left(-5+11-4\left(40-3\sqrt{3}\right)\right)$$

Add -5 and 11 to get 6.

$$19-2\left(6-4\left(40-3\sqrt{3}\right)\right)$$

Use the distributive property to multiply -4 by 40-3\sqrt{3}.

$$19-2\left(6-160+12\sqrt{3}\right)$$

Subtract 160 from 6 to get -154.

$$19-2\left(-154+12\sqrt{3}\right)$$

Use the distributive property to multiply -2 by -154+12\sqrt{3}.

$$19+308-24\sqrt{3}$$

Add 19 and 308 to get 327.

$$327-24\sqrt{3}$$