Algebra Examples

$\sqrt{t^{2}} = 0$

Step 1

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

${\sqrt{t^{2}}}^{2} = 0^{2}$

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 $\sqrt{t^{2}}$ as $t^{\frac{2}{2}}$ .

${(t^{\frac{2}{2}})}^{2} = 0^{2}$

Step 2.2

Divide $2$ by $2$ .

${(t^{1})}^{2} = 0^{2}$

Step 2.3

Simplify the left side.

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Step 2.3.1

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

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Step 2.3.1.1

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

$t^{1 \cdot 2} = 0^{2}$

Step 2.3.1.2

Multiply $2$ by $1$ .

$t^{2} = 0^{2}$

Step 2.4

Simplify the right side.

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Step 2.4.1

Raising $0$ to any positive power yields $0$ .

$t^{2} = 0$

Step 3

Solve for $t$ .

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Step 3.1

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

$t = \pm \sqrt{0}$

Step 3.2

Simplify $\pm \sqrt{0}$ .

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Step 3.2.1

Rewrite $0$ as $0^{2}$ .

$t = \pm \sqrt{0^{2}}$

Step 3.2.2

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

$t = \pm 0$

Step 3.2.3

Plus or minus $0$ is $0$ .

$t = 0$