How to solve 3 3 h 5 3 5

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 3 3 h 5 3 5 | Equatix

Question

$$\sqrt { 2 \frac { 1 } { 3 } \div \{ 1 \frac { 1 } { 3 } + ( 1 \frac { 3 } { 4 } \times 3 \frac { 1 } { 5 } - 3 \frac { 1 } { 5 } ) \} \times 1 \frac { 1 } { 5 } }$$

Evaluate

$\frac{\sqrt{3}}{2}\approx 0.866025404$

Solution Steps

Multiply $2$ and $3$ to get $6$.

$$\sqrt{\frac{\frac{6+1}{3}}{\frac{1\times 3+1}{3}+\frac{1\times 4+3}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $6$ and $1$ to get $7$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{1\times 3+1}{3}+\frac{1\times 4+3}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Multiply $1$ and $3$ to get $3$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{3+1}{3}+\frac{1\times 4+3}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $3$ and $1$ to get $4$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{1\times 4+3}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Multiply $1$ and $4$ to get $4$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{4+3}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $4$ and $3$ to get $7$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{7}{4}\times \frac{3\times 5+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

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

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{7}{4}\times \frac{15+1}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $15$ and $1$ to get $16$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{7}{4}\times \frac{16}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Multiply $\frac{7}{4}$ times $\frac{16}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{7\times 16}{4\times 5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Do the multiplications in the fraction $\frac{7\times 16}{4\times 5}$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{112}{20}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Reduce the fraction $\frac{112}{20}$ to lowest terms by extracting and canceling out $4$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{4}{3}+\frac{28}{5}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Least common multiple of $3$ and $5$ is $15$. Convert $\frac{4}{3}$ and $\frac{28}{5}$ to fractions with denominator $15$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{20}{15}+\frac{84}{15}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Since $\frac{20}{15}$ and $\frac{84}{15}$ have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{7}{3}}{\frac{20+84}{15}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $20$ and $84$ to get $104$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{104}{15}-\frac{3\times 5+1}{5}}\times \frac{1\times 5+1}{5}}$$

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

$$\sqrt{\frac{\frac{7}{3}}{\frac{104}{15}-\frac{15+1}{5}}\times \frac{1\times 5+1}{5}}$$

Add $15$ and $1$ to get $16$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{104}{15}-\frac{16}{5}}\times \frac{1\times 5+1}{5}}$$

Least common multiple of $15$ and $5$ is $15$. Convert $\frac{104}{15}$ and $\frac{16}{5}$ to fractions with denominator $15$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{104}{15}-\frac{48}{15}}\times \frac{1\times 5+1}{5}}$$

Since $\frac{104}{15}$ and $\frac{48}{15}$ have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{7}{3}}{\frac{104-48}{15}}\times \frac{1\times 5+1}{5}}$$

Subtract $48$ from $104$ to get $56$.

$$\sqrt{\frac{\frac{7}{3}}{\frac{56}{15}}\times \frac{1\times 5+1}{5}}$$

Divide $\frac{7}{3}$ by $\frac{56}{15}$ by multiplying $\frac{7}{3}$ by the reciprocal of $\frac{56}{15}$.

$$\sqrt{\frac{7}{3}\times \frac{15}{56}\times \frac{1\times 5+1}{5}}$$

Multiply $\frac{7}{3}$ times $\frac{15}{56}$ by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{7\times 15}{3\times 56}\times \frac{1\times 5+1}{5}}$$

Do the multiplications in the fraction $\frac{7\times 15}{3\times 56}$.

$$\sqrt{\frac{105}{168}\times \frac{1\times 5+1}{5}}$$

Reduce the fraction $\frac{105}{168}$ to lowest terms by extracting and canceling out $21$.

$$\sqrt{\frac{5}{8}\times \frac{1\times 5+1}{5}}$$

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

$$\sqrt{\frac{5}{8}\times \frac{5+1}{5}}$$

Add $5$ and $1$ to get $6$.

$$\sqrt{\frac{5}{8}\times \frac{6}{5}}$$

Multiply $\frac{5}{8}$ times $\frac{6}{5}$ by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{5\times 6}{8\times 5}}$$

Cancel out $5$ in both numerator and denominator.

$$\sqrt{\frac{6}{8}}$$

Reduce the fraction $\frac{6}{8}$ to lowest terms by extracting and canceling out $2$.

$$\sqrt{\frac{3}{4}}$$

Rewrite the square root of the division $\sqrt{\frac{3}{4}}$ as the division of square roots $\frac{\sqrt{3}}{\sqrt{4}}$.

$$\frac{\sqrt{3}}{\sqrt{4}}$$

Calculate the square root of $4$ and get $2$.

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

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