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Simplify (6 square root of 18)÷4 square root of 3

$6 \sqrt{18} \div 4 \sqrt{3}$

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt{18}}{4 \sqrt{3}}$

Step 2

Cancel the common factor of

$6$ and

$4$ .

Factor

$2$ out of

$6 \sqrt{18}$ .

$\frac{2 (3 \sqrt{18})}{4 \sqrt{3}}$

Cancel the common factors.

Factor

$2$ out of

$4 \sqrt{3}$ .

$\frac{2 (3 \sqrt{18})}{2 (2 \sqrt{3})}$

Cancel the common factor.

$\frac{2 (3 \sqrt{18})}{2 (2 \sqrt{3})}$

Rewrite the expression.

$\frac{3 \sqrt{18}}{2 \sqrt{3}}$

$\frac{3 \sqrt{18}}{2 \sqrt{3}}$

$\frac{3 \sqrt{18}}{2 \sqrt{3}}$

Step 3

Combine

$\sqrt{18}$ and

$\sqrt{3}$ into a single radical.

$\frac{3 \sqrt{\frac{18}{3}}}{2}$

Step 4

Cancel the common factor of

$18$ and

$3$ .

Factor

$3$ out of

$18$ .

$\frac{3 \sqrt{\frac{3 \cdot 6}{3}}}{2}$

Cancel the common factors.

Factor

$3$ out of

$3$ .

$\frac{3 \sqrt{\frac{3 \cdot 6}{3 (1)}}}{2}$

Cancel the common factor.

$\frac{3 \sqrt{\frac{3 \cdot 6}{3 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{3 \sqrt{\frac{6}{1}}}{2}$

Divide

$6$ by

$1$ .

$\frac{3 \sqrt{6}}{2}$

$\frac{3 \sqrt{6}}{2}$

$\frac{3 \sqrt{6}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \sqrt{6}}{2}$

Decimal Form:

$3.67423461 \dots$

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