Solve for s square root of s^2 = square root of 1040

$\sqrt{s^{2}} = \sqrt{1040}$

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

${\sqrt{s^{2}}}^{2} = {\sqrt{1040}}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${(s^{1})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$s^{1 \cdot 2} = {\sqrt{1040}}^{2}$

Multiply $2$ by $1$ .

$s^{2} = {\sqrt{1040}}^{2}$

Rewrite $1040$ as $4^{2} \cdot 65$ .

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Factor $16$ out of $1040$ .

$s^{2} = {\sqrt{16 (65)}}^{2}$

Rewrite $16$ as $4^{2}$ .

$s^{2} = {\sqrt{4^{2} \cdot 65}}^{2}$

Pull terms out from under the radical.

$s^{2} = {(4 \sqrt{65})}^{2}$

Apply the product rule to $4 \sqrt{65}$ .

$s^{2} = 4^{2} {\sqrt{65}}^{2}$

Raise $4$ to the power of $2$ .

$s^{2} = 16 {\sqrt{65}}^{2}$

Rewrite ${\sqrt{65}}^{2}$ as $65$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{65}$ as $65^{\frac{1}{2}}$ .

$s^{2} = 16 {(65^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$s^{2} = 16 \cdot 65^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$s^{2} = 16 \cdot 65^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$s^{2} = 16 \cdot 65^{\frac{2}{2}}$

Divide $1$ by $1$ .

$s^{2} = 16 \cdot 65^{1}$

Evaluate the exponent.

$s^{2} = 16 \cdot 65$

Multiply $16$ by $65$ .

$s^{2} = 1040$

Solve for $s$ .

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

$s = \pm \sqrt{1040}$

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

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Simplify the right side of the equation.

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Rewrite $1040$ as $4^{2} \cdot 65$ .

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Factor $16$ out of $1040$ .

$s = \pm \sqrt{16 (65)}$

Rewrite $16$ as $4^{2}$ .

$s = \pm \sqrt{4^{2} \cdot 65}$

Pull terms out from under the radical.

$s = \pm 4 \sqrt{65}$

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

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First, use the positive value of the $\pm$ to find the first solution.

$s = 4 \sqrt{65}$

Next, use the negative value of the $\pm$ to find the second solution.

$s = - 4 \sqrt{65}$

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

$s = 4 \sqrt{65}, - 4 \sqrt{65}$

The result can be shown in multiple forms.

Exact Form:

$s = 4 \sqrt{65}, - 4 \sqrt{65}$

Decimal Form:

$s = 32.24903099 \dots, - 32.24903099 \dots$

Solve for s square root of s^2 = square root of 1040

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