Basic Math Examples

\sqrt{1521} = \sqrt{c^{2}}

$\sqrt{1521} = \sqrt{c^{2}}$

Step 1

Rewrite the equation as

\sqrt{c^{2}} = \sqrt{1521}

$\sqrt{c^{2}} = \sqrt{1521}$ .

\sqrt{c^{2}} = \sqrt{1521}

$\sqrt{c^{2}} = \sqrt{1521}$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

{\sqrt{c^{2}}}^{2} = {\sqrt{1521}}^{2}

${\sqrt{c^{2}}}^{2} = {\sqrt{1521}}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{c^{2}}

$\sqrt{c^{2}}$ as

c^{\frac{2}{2}}

$c^{\frac{2}{2}}$ .

{(c^{\frac{2}{2}})}^{2} = {\sqrt{1521}}^{2}

${(c^{\frac{2}{2}})}^{2} = {\sqrt{1521}}^{2}$

Step 3.2

Divide

2

$2$ by

2

$2$ .

{(c^{1})}^{2} = {\sqrt{1521}}^{2}

${(c^{1})}^{2} = {\sqrt{1521}}^{2}$

Step 3.3

Simplify the left side.

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Step 3.3.1

Multiply the exponents in

{(c^{1})}^{2}

${(c^{1})}^{2}$ .

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Step 3.3.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

c^{1 \cdot 2} = {\sqrt{1521}}^{2}

$c^{1 \cdot 2} = {\sqrt{1521}}^{2}$

Step 3.3.1.2

Multiply

2

$2$ by

1

$1$ .

c^{2} = {\sqrt{1521}}^{2}

$c^{2} = {\sqrt{1521}}^{2}$

c^{2} = {\sqrt{1521}}^{2}

$c^{2} = {\sqrt{1521}}^{2}$

c^{2} = {\sqrt{1521}}^{2}

$c^{2} = {\sqrt{1521}}^{2}$

Step 3.4

Simplify the right side.

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Step 3.4.1

Simplify

{\sqrt{1521}}^{2}

${\sqrt{1521}}^{2}$ .

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Step 3.4.1.1

Rewrite

1521

$1521$ as

39^{2}

$39^{2}$ .

c^{2} = {\sqrt{39^{2}}}^{2}

$c^{2} = {\sqrt{39^{2}}}^{2}$

Step 3.4.1.2

Pull terms out from under the radical, assuming positive real numbers.

c^{2} = 39^{2}

$c^{2} = 39^{2}$

Step 3.4.1.3

Raise

39

$39$ to the power of

2

$2$ .

c^{2} = 1521

$c^{2} = 1521$

c^{2} = 1521

$c^{2} = 1521$

c^{2} = 1521

$c^{2} = 1521$

c^{2} = 1521

$c^{2} = 1521$

Step 4

Solve for

c

$c$ .

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Step 4.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

c = \pm \sqrt{1521}

$c = \pm \sqrt{1521}$

Step 4.2

Simplify

\pm \sqrt{1521}

$\pm \sqrt{1521}$ .

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Step 4.2.1

Rewrite

1521

$1521$ as

39^{2}

$39^{2}$ .

c = \pm \sqrt{39^{2}}

$c = \pm \sqrt{39^{2}}$

Step 4.2.2

Pull terms out from under the radical, assuming positive real numbers.

c = \pm 39

$c = \pm 39$

c = \pm 39

$c = \pm 39$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.3.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

c = 39

$c = 39$

Step 4.3.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

c = - 39

$c = - 39$

Step 4.3.3

The complete solution is the result of both the positive and negative portions of the solution.

c = 39, - 39

$c = 39, - 39$

c = 39, - 39

$c = 39, - 39$

c = 39, - 39

$c = 39, - 39$