Evaluate -1/7 square root of 147

$- \frac{1}{7} \sqrt{147}$

Step 1

Rewrite $147$ as $7^{2} \cdot 3$ .

Factor $49$ out of $147$ .

$- \frac{1}{7} \cdot \sqrt{49 (3)}$

Rewrite $49$ as $7^{2}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{1}{7}$ into the numerator.

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

Factor $7$ out of $7 \sqrt{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 1 \cdot \sqrt{3}$

Step 4

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$- \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{3}$

Decimal Form:

$- 1.73205080 \dots$