Simplify (5 square root of 63)÷6 square root of 7

$5 \sqrt{63} \div 6 \sqrt{7}$

Rewrite the division as a fraction.

$\frac{5 \sqrt{63}}{6 \sqrt{7}}$

Combine $\sqrt{63}$ and $\sqrt{7}$ into a single radical.

$\frac{5 \sqrt{\frac{63}{7}}}{6}$

Cancel the common factor of $63$ and $7$ .

Factor $7$ out of $63$ .

$\frac{5 \sqrt{\frac{7 \cdot 9}{7}}}{6}$

Cancel the common factors.

Factor $7$ out of $7$ .

$\frac{5 \sqrt{\frac{7 \cdot 9}{7 (1)}}}{6}$

Cancel the common factor.

$\frac{5 \sqrt{\frac{7 \cdot 9}{7 \cdot 1}}}{6}$

Rewrite the expression.

$\frac{5 \sqrt{\frac{9}{1}}}{6}$

Divide $9$ by $1$ .

$\frac{5 \sqrt{9}}{6}$

Simplify the numerator.

Rewrite $9$ as $3^{2}$ .

$\frac{5 \sqrt{3^{2}}}{6}$

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

$\frac{5 \cdot 3}{6}$

Reduce the expression by cancelling the common factors.

Multiply $5$ by $3$ .

$\frac{15}{6}$

Cancel the common factor of $15$ and $6$ .

Factor $3$ out of $15$ .

$\frac{3 (5)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$\frac{3 \cdot 5}{3 \cdot 2}$

Cancel the common factor.

$\frac{3 \cdot 5}{3 \cdot 2}$

Rewrite the expression.

$\frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$