Evaluate square root of 27- square root of 147

$\sqrt{27} - \sqrt{147}$

Step 1

Simplify each term.

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$\sqrt{9 (3)} - \sqrt{147}$

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

$\sqrt{3^{2} \cdot 3} - \sqrt{147}$

$\sqrt{3^{2} \cdot 3} - \sqrt{147}$

Pull terms out from under the radical.

$3 \sqrt{3} - \sqrt{147}$

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

Factor $49$ out of $147$ .

$3 \sqrt{3} - \sqrt{49 (3)}$

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

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

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

Pull terms out from under the radical.

$3 \sqrt{3} - (7 \sqrt{3})$

Multiply $7$ by $- 1$ .

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

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

Step 2

Subtract $7 \sqrt{3}$ from $3 \sqrt{3}$ .

$- 4 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt{3}$

Decimal Form:

$- 6.92820323 \dots$

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