Solve Asqrt{25/2}-sqrt{9/4}=

$$A \sqrt { \frac { 25 } { 2 } } - \sqrt { \frac { 9 } { 4 } } =$$

Evaluate

$$\frac{5\sqrt{2}A-3}{2}$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{25}{2}} as the division of square roots \frac{\sqrt{25}}{\sqrt{2}}.

$$A\times \frac{\sqrt{25}}{\sqrt{2}}-\sqrt{\frac{9}{4}}$$

Calculate the square root of 25 and get 5.

$$A\times \frac{5}{\sqrt{2}}-\sqrt{\frac{9}{4}}$$

Rationalize the denominator of \frac{5}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$A\times \frac{5\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\sqrt{\frac{9}{4}}$$

The square of \sqrt{2} is 2.

$$A\times \frac{5\sqrt{2}}{2}-\sqrt{\frac{9}{4}}$$

Express A\times \frac{5\sqrt{2}}{2} as a single fraction.

$$\frac{A\times 5\sqrt{2}}{2}-\sqrt{\frac{9}{4}}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{A\times 5\sqrt{2}}{2}-\frac{3}{2}$$

Since \frac{A\times 5\sqrt{2}}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{A\times 5\sqrt{2}-3}{2}$$

Do the multiplications in A\times 5\sqrt{2}-3.

$$\frac{5A\sqrt{2}-3}{2}$$

Differentiate w.r.t. A

$$\frac{5 \sqrt{2}}{2} = 3.5355339059327378$$