Solve sqrt{5^2-3^2}+(-12:2.3):(-3)^2

$$\sqrt { 5 ^ { 2 } - 3 ^ { 2 } } + ( - 12 : 2.3 ) : ( - 3 ) ^ { 2 }$$

Evaluate

$$\frac{236}{69}\approx 3.420289855$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25-3^{2}}+\frac{\frac{-12}{2.3}}{\left(-3\right)^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{25-9}+\frac{\frac{-12}{2.3}}{\left(-3\right)^{2}}$$

Subtract 9 from 25 to get 16.

$$\sqrt{16}+\frac{\frac{-12}{2.3}}{\left(-3\right)^{2}}$$

Calculate the square root of 16 and get 4.

$$4+\frac{\frac{-12}{2.3}}{\left(-3\right)^{2}}$$

Expand \frac{-12}{2.3} by multiplying both numerator and the denominator by 10.

$$4+\frac{\frac{-120}{23}}{\left(-3\right)^{2}}$$

Fraction \frac{-120}{23} can be rewritten as -\frac{120}{23} by extracting the negative sign.

$$4+\frac{-\frac{120}{23}}{\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$4+\frac{-\frac{120}{23}}{9}$$

Express \frac{-\frac{120}{23}}{9} as a single fraction.

$$4+\frac{-120}{23\times 9}$$

Multiply 23 and 9 to get 207.

$$4+\frac{-120}{207}$$

Reduce the fraction \frac{-120}{207} to lowest terms by extracting and canceling out 3.

$$4-\frac{40}{69}$$

Convert 4 to fraction \frac{276}{69}.

$$\frac{276}{69}-\frac{40}{69}$$

Since \frac{276}{69} and \frac{40}{69} have the same denominator, subtract them by subtracting their numerators.

$$\frac{276-40}{69}$$

Subtract 40 from 276 to get 236.

$$\frac{236}{69}$$

Factor

$$\frac{59 \cdot 2 ^ {2}}{3 \cdot 23} = 3\frac{29}{69} = 3.420289855072464$$