Solve =7th root of 128 300^ 1 12 =12th root of 300 | 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

$$=7th\ root\ of\ 128\ 300^{\frac{1}{12}}=12th\ root\ of\ 300$$

Solve for h (complex solution)

$\left\{\begin{matrix}\\h=\frac{6\sqrt{1283}h_{300}}{44905}\text{, }&\text{unconditionally}\\h\in \mathrm{C}\text{, }&t=0\end{matrix}\right.$

Steps for Solving Linear Equation

Reorder the terms.

$$7\sqrt{128300}ht=12h_{300}t$$

Factor $128300=10^{2}\times 1283$. Rewrite the square root of the product $\sqrt{10^{2}\times 1283}$ as the product of square roots $\sqrt{10^{2}}\sqrt{1283}$. Take the square root of $10^{2}$.

$$7\times 10\sqrt{1283}ht=12h_{300}t$$

Multiply $7$ and $10$ to get $70$.

$$70\sqrt{1283}ht=12h_{300}t$$

The equation is in standard form.

$$70\sqrt{1283}th=12h_{300}t$$

Divide both sides by $70\sqrt{1283}t$.

$$\frac{70\sqrt{1283}th}{70\sqrt{1283}t}=\frac{12h_{300}t}{70\sqrt{1283}t}$$

Dividing by $70\sqrt{1283}t$ undoes the multiplication by $70\sqrt{1283}t$.

$$h=\frac{12h_{300}t}{70\sqrt{1283}t}$$

Divide $12th_{300}$ by $70\sqrt{1283}t$.

$$h=\frac{6\sqrt{1283}h_{300}}{44905}$$

Solve for h_300 (complex solution)

$\left\{\begin{matrix}\\h_{300}=\frac{35\sqrt{1283}h}{6}\text{, }&\text{unconditionally}\\h_{300}\in \mathrm{C}\text{, }&t=0\end{matrix}\right.$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$12th_{300}=7th\times 128300^{\frac{1}{2}}$$

Reorder the terms.

$$12h_{300}t=7\sqrt{128300}ht$$

Factor $128300=10^{2}\times 1283$. Rewrite the square root of the product $\sqrt{10^{2}\times 1283}$ as the product of square roots $\sqrt{10^{2}}\sqrt{1283}$. Take the square root of $10^{2}$.

$$12h_{300}t=7\times 10\sqrt{1283}ht$$

Multiply $7$ and $10$ to get $70$.

$$12h_{300}t=70\sqrt{1283}ht$$

The equation is in standard form.

$$12th_{300}=70\sqrt{1283}ht$$

Divide both sides by $12t$.

$$\frac{12th_{300}}{12t}=\frac{70\sqrt{1283}ht}{12t}$$

Dividing by $12t$ undoes the multiplication by $12t$.

$$h_{300}=\frac{70\sqrt{1283}ht}{12t}$$

Divide $70\sqrt{1283}ht$ by $12t$.

$$h_{300}=\frac{35\sqrt{1283}h}{6}$$

Solve for h

$\left\{\begin{matrix}\\h=\frac{6\sqrt{1283}h_{300}}{44905}\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$

Steps for Solving Linear Equation

Reorder the terms.

$$7\sqrt{128300}ht=12h_{300}t$$

Factor $128300=10^{2}\times 1283$. Rewrite the square root of the product $\sqrt{10^{2}\times 1283}$ as the product of square roots $\sqrt{10^{2}}\sqrt{1283}$. Take the square root of $10^{2}$.

$$7\times 10\sqrt{1283}ht=12h_{300}t$$

Multiply $7$ and $10$ to get $70$.

$$70\sqrt{1283}ht=12h_{300}t$$

The equation is in standard form.

$$70\sqrt{1283}th=12h_{300}t$$

Divide both sides by $70\sqrt{1283}t$.

$$\frac{70\sqrt{1283}th}{70\sqrt{1283}t}=\frac{12h_{300}t}{70\sqrt{1283}t}$$

Dividing by $70\sqrt{1283}t$ undoes the multiplication by $70\sqrt{1283}t$.

$$h=\frac{12h_{300}t}{70\sqrt{1283}t}$$

Divide $12th_{300}$ by $70\sqrt{1283}t$.

$$h=\frac{6\sqrt{1283}h_{300}}{44905}$$

Solve for h_300

$\left\{\begin{matrix}\\h_{300}=\frac{35\sqrt{1283}h}{6}\text{, }&\text{unconditionally}\\h_{300}\in \mathrm{R}\text{, }&t=0\end{matrix}\right.$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$12th_{300}=7th\times 128300^{\frac{1}{2}}$$

Reorder the terms.

$$12h_{300}t=7\sqrt{128300}ht$$

Factor $128300=10^{2}\times 1283$. Rewrite the square root of the product $\sqrt{10^{2}\times 1283}$ as the product of square roots $\sqrt{10^{2}}\sqrt{1283}$. Take the square root of $10^{2}$.

$$12h_{300}t=7\times 10\sqrt{1283}ht$$

Multiply $7$ and $10$ to get $70$.

$$12h_{300}t=70\sqrt{1283}ht$$

The equation is in standard form.

$$12th_{300}=70\sqrt{1283}ht$$

Divide both sides by $12t$.

$$\frac{12th_{300}}{12t}=\frac{70\sqrt{1283}ht}{12t}$$

Dividing by $12t$ undoes the multiplication by $12t$.

$$h_{300}=\frac{70\sqrt{1283}ht}{12t}$$

Divide $70\sqrt{1283}ht$ by $12t$.

$$h_{300}=\frac{35\sqrt{1283}h}{6}$$