Simplify -(42 square root of 30)/(12 square root of 10)

$- \frac{42 \sqrt{30}}{12 \sqrt{10}}$

Cancel the common factor of $42$ and $12$ .

Factor $6$ out of $42 \sqrt{30}$ .

$- \frac{6 (7 \sqrt{30})}{12 \sqrt{10}}$

Cancel the common factors.

Factor $6$ out of $12 \sqrt{10}$ .

$- \frac{6 (7 \sqrt{30})}{6 (2 \sqrt{10})}$

Cancel the common factor.

$- \frac{6 (7 \sqrt{30})}{6 (2 \sqrt{10})}$

Rewrite the expression.

$- \frac{7 \sqrt{30}}{2 \sqrt{10}}$

Combine $\sqrt{30}$ and $\sqrt{10}$ into a single radical.

$- \frac{7 \sqrt{\frac{30}{10}}}{2}$

Cancel the common factor of $30$ and $10$ .

Factor $10$ out of $30$ .

$- \frac{7 \sqrt{\frac{10 \cdot 3}{10}}}{2}$

Cancel the common factors.

Factor $10$ out of $10$ .

$- \frac{7 \sqrt{\frac{10 \cdot 3}{10 (1)}}}{2}$

Cancel the common factor.

$- \frac{7 \sqrt{\frac{10 \cdot 3}{10 \cdot 1}}}{2}$

Rewrite the expression.

$- \frac{7 \sqrt{\frac{3}{1}}}{2}$

Divide $3$ by $1$ .

$- \frac{7 \sqrt{3}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 \sqrt{3}}{2}$

Decimal Form:

$- 6.06217782 \dots$