Solve 1.5/3(20+1.5+sqrt{20*1.5)}

$$\frac{ 1.5 }{ 3 } (20+1.5+ \sqrt{ 20 \times 1.5) }$$

Evaluate

$$\frac{\sqrt{30}}{2}+10.75\approx 13.488612788$$

Solution Steps

Expand \frac{1.5}{3} by multiplying both numerator and the denominator by 10.

$$\frac{15}{30}\left(20+1.5+\sqrt{20\times 1.5}\right)$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{1}{2}\left(20+1.5+\sqrt{20\times 1.5}\right)$$

Add 20 and 1.5 to get 21.5.

$$\frac{1}{2}\left(21.5+\sqrt{20\times 1.5}\right)$$

Multiply 20 and 1.5 to get 30.

$$\frac{1}{2}\left(21.5+\sqrt{30}\right)$$

Use the distributive property to multiply \frac{1}{2} by 21.5+\sqrt{30}.

$$\frac{1}{2}\times 21.5+\frac{1}{2}\sqrt{30}$$

Convert decimal number 21.5 to fraction \frac{215}{10}. Reduce the fraction \frac{215}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}\times \frac{43}{2}+\frac{1}{2}\sqrt{30}$$

Multiply \frac{1}{2} times \frac{43}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 43}{2\times 2}+\frac{1}{2}\sqrt{30}$$

Do the multiplications in the fraction \frac{1\times 43}{2\times 2}.

$$\frac{43}{4}+\frac{1}{2}\sqrt{30}$$