Solve 1/3*(7.29+sqrt{0.36*7.29}+0.36)*0.3

$$\frac { 1 } { 3 } \times ( 7.29 + \sqrt { 0.36 \times 7.29 } + 0.36 ) \times 0.3$$

Evaluate

$$0.927$$

Solution Steps

Convert decimal number 0.3 to fraction \frac{3}{10}.

$$\frac{3}{10}\times \frac{1}{3}\left(7.29+\sqrt{0.36\times 7.29}+0.36\right)$$

Multiply \frac{3}{10} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{10\times 3}\left(7.29+\sqrt{0.36\times 7.29}+0.36\right)$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{10}\left(7.29+\sqrt{0.36\times 7.29}+0.36\right)$$

Multiply 0.36 and 7.29 to get 2.6244.

$$\frac{1}{10}\left(7.29+\sqrt{2.6244}+0.36\right)$$

Calculate the square root of 2.6244 and get 1.62.

$$\frac{1}{10}\left(7.29+1.62+0.36\right)$$

Add 7.29 and 1.62 to get 8.91.

$$\frac{1}{10}\left(8.91+0.36\right)$$

Add 8.91 and 0.36 to get 9.27.

$$\frac{1}{10}\times 9.27$$

Convert decimal number 9.27 to fraction \frac{927}{100}.

$$\frac{1}{10}\times \frac{927}{100}$$

Multiply \frac{1}{10} times \frac{927}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 927}{10\times 100}$$

Do the multiplications in the fraction \frac{1\times 927}{10\times 100}.

$$\frac{927}{1000}$$

Factor

$$\frac{103 \cdot 3 ^ {2}}{2 ^ {3} \cdot 5 ^ {3}} = 0.927$$