Solve 2 3/4 * sqrt(5/2) of 3 3/5 + (1 2/5) / (2/3); 3/5 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$2 \frac { 3 } { 4 } \sqrt { \frac { 5 } { 2 } } 3 \frac { 3 } { 5 } + 1 \frac { 2 } { 5 } \div \frac { 2 } { 3 } \frac { 3 } { 5 }$$

Evaluate

$\frac{99\sqrt{10}}{20}+\frac{63}{50}\approx 16.913274418$

Short Solution Steps

Multiply $2$ and $4$ to get $8$.

$$\frac{8+3}{4}\sqrt{\frac{5}{2}}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Add $8$ and $3$ to get $11$.

$$\frac{11}{4}\sqrt{\frac{5}{2}}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Rewrite the square root of the division $\sqrt{\frac{5}{2}}$ as the division of square roots $\frac{\sqrt{5}}{\sqrt{2}}$.

$$\frac{11}{4}\times \frac{\sqrt{5}}{\sqrt{2}}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

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

$$\frac{11}{4}\times \frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

The square of $\sqrt{2}$ is $2$.

$$\frac{11}{4}\times \frac{\sqrt{5}\sqrt{2}}{2}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

To multiply $\sqrt{5}$ and $\sqrt{2}$, multiply the numbers under the square root.

$$\frac{11}{4}\times \frac{\sqrt{10}}{2}\times \frac{3\times 5+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Multiply $3$ and $5$ to get $15$.

$$\frac{11}{4}\times \frac{\sqrt{10}}{2}\times \frac{15+3}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Add $15$ and $3$ to get $18$.

$$\frac{11}{4}\times \frac{\sqrt{10}}{2}\times \frac{18}{5}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Multiply $\frac{11}{4}$ times $\frac{18}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 18}{4\times 5}\times \frac{\sqrt{10}}{2}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Do the multiplications in the fraction $\frac{11\times 18}{4\times 5}$.

$$\frac{198}{20}\times \frac{\sqrt{10}}{2}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Reduce the fraction $\frac{198}{20}$ to lowest terms by extracting and canceling out $2$.

$$\frac{99}{10}\times \frac{\sqrt{10}}{2}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Multiply $\frac{99}{10}$ times $\frac{\sqrt{10}}{2}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{\frac{1\times 5+2}{5}}{\frac{2}{3}}\times \frac{3}{5}$$

Divide $\frac{1\times 5+2}{5}$ by $\frac{2}{3}$ by multiplying $\frac{1\times 5+2}{5}$ by the reciprocal of $\frac{2}{3}$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{\left(1\times 5+2\right)\times 3}{5\times 2}\times \frac{3}{5}$$

Multiply $1$ and $5$ to get $5$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{\left(5+2\right)\times 3}{5\times 2}\times \frac{3}{5}$$

Add $5$ and $2$ to get $7$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{7\times 3}{5\times 2}\times \frac{3}{5}$$

Multiply $7$ and $3$ to get $21$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{21}{5\times 2}\times \frac{3}{5}$$

Multiply $5$ and $2$ to get $10$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{21}{10}\times \frac{3}{5}$$

Multiply $\frac{21}{10}$ times $\frac{3}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{21\times 3}{10\times 5}$$

Do the multiplications in the fraction $\frac{21\times 3}{10\times 5}$.

$$\frac{99\sqrt{10}}{10\times 2}+\frac{63}{50}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $10\times 2$ and $50$ is $100$. Multiply $\frac{99\sqrt{10}}{10\times 2}$ times $\frac{5}{5}$. Multiply $\frac{63}{50}$ times $\frac{2}{2}$.

$$\frac{5\times 99\sqrt{10}}{100}+\frac{63\times 2}{100}$$

Since $\frac{5\times 99\sqrt{10}}{100}$ and $\frac{63\times 2}{100}$ have the same denominator, add them by adding their numerators.

$$\frac{5\times 99\sqrt{10}+63\times 2}{100}$$

Do the multiplications in $5\times 99\sqrt{10}+63\times 2$.

$$\frac{495\sqrt{10}+126}{100}$$

Factor

$\frac{9 {(55 \sqrt{10} + 14)}}{100} = 16.913274417833478$