Simplify the Radical Expression 4 square root of 3*3 square root of 3

$4 \sqrt{3} \cdot 3 \sqrt{3}$

Step 1

Multiply $3$ by $4$ .

$12 \sqrt{3} \sqrt{3}$

Step 2

Multiply $12 \sqrt{3} \sqrt{3}$ .

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

$12 ({\sqrt{3}}^{1} \sqrt{3})$

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

$12 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$12 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$12 {\sqrt{3}}^{2}$

Step 3

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

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

$12 {(3^{\frac{1}{2}})}^{2}$

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

$12 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$12 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$12 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$12 \cdot 3^{1}$

Evaluate the exponent.

$12 \cdot 3$

Step 4

Multiply $12$ by $3$ .

$36$