Simplify (21 square root of 5)/(-7 square root of 125)

$\frac{21 \sqrt{5}}{- 7 \sqrt{125}}$

Step 1

Cancel the common factor of $21$ and $- 7$ .

Factor $7$ out of $21 \sqrt{5}$ .

$\frac{7 (3 \sqrt{5})}{- 7 \sqrt{125}}$

Cancel the common factors.

Factor $7$ out of $- 7 \sqrt{125}$ .

$\frac{7 (3 \sqrt{5})}{7 (- \sqrt{125})}$

Cancel the common factor.

$\frac{7 (3 \sqrt{5})}{7 (- \sqrt{125})}$

Rewrite the expression.

$\frac{3 \sqrt{5}}{- \sqrt{125}}$

Step 2

Combine $\sqrt{5}$ and $\sqrt{125}$ into a single radical.

$\frac{3 \sqrt{\frac{5}{125}}}{- 1}$

Step 3

Cancel the common factor of $5$ and $125$ .

Factor $5$ out of $5$ .

$\frac{3 \sqrt{\frac{5 (1)}{125}}}{- 1}$

Cancel the common factors.

Factor $5$ out of $125$ .

$\frac{3 \sqrt{\frac{5 \cdot 1}{5 \cdot 25}}}{- 1}$

Cancel the common factor.

$\frac{3 \sqrt{\frac{5 \cdot 1}{5 \cdot 25}}}{- 1}$

Rewrite the expression.

$\frac{3 \sqrt{\frac{1}{25}}}{- 1}$

Step 4

Simplify the expression.

Move the negative one from the denominator of $\frac{3 \sqrt{\frac{1}{25}}}{- 1}$ .

$- 1 \cdot (3 \sqrt{\frac{1}{25}})$

Rewrite $- 1 \cdot (3 \sqrt{\frac{1}{25}})$ as $- (3 \sqrt{\frac{1}{25}})$ .

$- (3 \sqrt{\frac{1}{25}})$

Step 5

Rewrite $\sqrt{\frac{1}{25}}$ as $\frac{\sqrt{1}}{\sqrt{25}}$ .

$- (3 \frac{\sqrt{1}}{\sqrt{25}})$

Step 6

Any root of $1$ is $1$ .

$- (3 \frac{1}{\sqrt{25}})$

Step 7

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

$- (3 \frac{1}{\sqrt{5^{2}}})$

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

$- (3 (\frac{1}{5}))$

Step 8

Combine $3$ and $\frac{1}{5}$ .

$- \frac{3}{5}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{5}$

Decimal Form:

$- 0.6$

Simplify (21 square root of 5)/(-7 square root of 125)

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