Simplify square root of 3t square root of 3t

$\sqrt{3 t} \sqrt{3 t}$

Step 1

Multiply $\sqrt{3 t} \sqrt{3 t}$ .

Raise $\sqrt{3 t}$ to the power of $1$ .

${\sqrt{3 t}}^{1} \sqrt{3 t}$

Raise $\sqrt{3 t}$ to the power of $1$ .

${\sqrt{3 t}}^{1} {\sqrt{3 t}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\sqrt{3 t}}^{1 + 1}$

Add $1$ and $1$ .

${\sqrt{3 t}}^{2}$

Step 2

Rewrite ${\sqrt{3 t}}^{2}$ as $3 t$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 t}$ as ${(3 t)}^{\frac{1}{2}}$ .

${({(3 t)}^{\frac{1}{2}})}^{2}$

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

${(3 t)}^{\frac{1}{2} \cdot 2}$

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

${(3 t)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 t)}^{\frac{2}{2}}$

Rewrite the expression.

${(3 t)}^{1}$

Simplify.

$3 t$