Solve (5^2+3*[-4+6div(-5+sqrt{16})])^2

$$( 5 ^ { 2 } + 3 \cdot [ - 4 + 6 \div ( - 5 + \sqrt { 16 } ) ] ) ^ { 2 }$$

Evaluate

$$25$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\left(25+3\left(-4+\frac{6}{-5+\sqrt{16}}\right)\right)^{2}$$

Calculate the square root of 16 and get 4.

$$\left(25+3\left(-4+\frac{6}{-5+4}\right)\right)^{2}$$

Add -5 and 4 to get -1.

$$\left(25+3\left(-4+\frac{6}{-1}\right)\right)^{2}$$

Fraction \frac{6}{-1} can be rewritten as -6 by extracting the negative sign.

$$\left(25+3\left(-4-6\right)\right)^{2}$$

Subtract 6 from -4 to get -10.

$$\left(25+3\left(-10\right)\right)^{2}$$

Multiply 3 and -10 to get -30.

$$\left(25-30\right)^{2}$$

Subtract 30 from 25 to get -5.

$$\left(-5\right)^{2}$$

Calculate -5 to the power of 2 and get 25.

$$25$$

Factor

$$5^{2}$$