Algebra Examples

$\sqrt{u} = - 5$

Step 1

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

${\sqrt{u}}^{2} = {(- 5)}^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${(u^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(u^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${(u^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

$u^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

$u^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

$u^{1} = {(- 5)}^{2}$

Step 2.2.1.2

Simplify.

$u = {(- 5)}^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $- 5$ to the power of $2$ .

$u = 25$

Step 3

Exclude the solutions that do not make $\sqrt{u} = - 5$ true.

$No solution$