$\frac{3+\sqrt{9+4\left(\frac{1}{3}\right)}}{2}$

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Algebra 2

Roots of integers

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\frac{3+\sqrt{9+4\left(\frac{1}{3}\right)}}{2}

Simplify Inside Square Root: First, let's simplify inside the square root: $9 + 4 \times \left(\frac{1}{3}\right)$ .
Addition and Common Denominator: $4 \times \left(\frac{1}{3}\right)$ equals $\frac{4}{3}$ .
Square Root of $\frac{31}{3}$ : Now, add $9$ and $\frac{4}{3}$ to get $9 + \frac{4}{3}.$
Final Simplification: $9$ can be written as $\frac{27}{3}$ to have a common denominator, so $\frac{27}{3} + \frac{4}{3}$ equals $\frac{31}{3}$ .
Final Simplification: $9$ can be written as $\frac{27}{3}$ to have a common denominator, so $\frac{27}{3} + \frac{4}{3}$ equals $\frac{31}{3}$ .Now we have $\sqrt{\frac{31}{3}}$ . Let's find the square root of $\frac{31}{3}$ .
Final Simplification: $9$ can be written as $\frac{27}{3}$ to have a common denominator, so $\frac{27}{3} + \frac{4}{3}$ equals $\frac{31}{3}$ .Now we have $\sqrt{\frac{31}{3}}$ . Let's find the square root of $\frac{31}{3}$ .The square root of $\frac{31}{3}$ is not a nice number, but we can leave it under the square root for now.
Final Simplification: $9$ can be written as $\frac{27}{3}$ to have a common denominator, so $\frac{27}{3} + \frac{4}{3}$ equals $\frac{31}{3}$ .Now we have $\sqrt{\frac{31}{3}}$ . Let's find the square root of $\frac{31}{3}$ .The square root of $\frac{31}{3}$ is not a nice number, but we can leave it under the square root for now.So we have $3 + \sqrt{\frac{31}{3}}$ . Now we need to divide this by $2$ .
Final Simplification: $9$ can be written as $27/3$ to have a common denominator, so $27/3 + 4/3$ equals $31/3$ .Now we have $\sqrt{31/3}$ . Let's find the square root of $31/3$ .The square root of $31/3$ is not a nice number, but we can leave it under the square root for now.So we have $3 + \sqrt{31/3}$ . Now we need to divide this by $2$ . $(3 + \sqrt{31/3}) / 2$ is the expression we need to simplify.
Final Simplification: $9$ can be written as $27/3$ to have a common denominator, so $27/3 + 4/3$ equals $31/3$ .Now we have $\sqrt{31/3}$ . Let's find the square root of $31/3$ .The square root of $31/3$ is not a nice number, but we can leave it under the square root for now.So we have $3 + \sqrt{31/3}$ . Now we need to divide this by $2$ . $(3 + \sqrt{31/3}) / 2$ is the expression we need to simplify.We can split the fraction into two parts: $27/3$ $0$ .
Final Simplification: $9$ can be written as $\frac{27}{3}$ to have a common denominator, so $\frac{27}{3} + \frac{4}{3}$ equals $\frac{31}{3}$ .Now we have $\sqrt{\frac{31}{3}}$ . Let's find the square root of $\frac{31}{3}$ .The square root of $\frac{31}{3}$ is not a nice number, but we can leave it under the square root for now.So we have $3 + \sqrt{\frac{31}{3}}$ . Now we need to divide this by $2$ .( $3 + \sqrt{\frac{31}{3}}$ ) / $2$ is the expression we need to simplify.We can split the fraction into two parts: $\frac{27}{3}$ $1$ + ( $\sqrt{\frac{31}{3}}$ )/ $2$ .Now we have our final simplified form: $\frac{27}{3}$ $1$ + ( $\sqrt{\frac{31}{3}}$ )/ $2$ .