Solve sqrt{3(2-5)^2+(7-4(2)^3/3)}

$$\sqrt { 3 ( 2 - 5 ) ^ { 2 } + ( \frac { 7 - 4 ( 2 ) ^ { 3 } } { 3 } ) }$$

Evaluate

$$\frac{2\sqrt{42}}{3}\approx 4.320493799$$

Solution Steps

Subtract 5 from 2 to get -3.

$$\sqrt{3\left(-3\right)^{2}+\frac{7-4\times 2^{3}}{3}}$$

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

$$\sqrt{3\times 9+\frac{7-4\times 2^{3}}{3}}$$

Multiply 3 and 9 to get 27.

$$\sqrt{27+\frac{7-4\times 2^{3}}{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\sqrt{27+\frac{7-4\times 8}{3}}$$

Multiply 4 and 8 to get 32.

$$\sqrt{27+\frac{7-32}{3}}$$

Subtract 32 from 7 to get -25.

$$\sqrt{27+\frac{-25}{3}}$$

Fraction \frac{-25}{3} can be rewritten as -\frac{25}{3} by extracting the negative sign.

$$\sqrt{27-\frac{25}{3}}$$

Subtract \frac{25}{3} from 27 to get \frac{56}{3}.

$$\sqrt{\frac{56}{3}}$$

Rewrite the square root of the division \sqrt{\frac{56}{3}} as the division of square roots \frac{\sqrt{56}}{\sqrt{3}}.

$$\frac{\sqrt{56}}{\sqrt{3}}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{2\sqrt{14}}{\sqrt{3}}$$

Rationalize the denominator of \frac{2\sqrt{14}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{2\sqrt{14}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{14}\sqrt{3}}{3}$$

To multiply \sqrt{14} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{2\sqrt{42}}{3}$$