Evaluate square root of 147- square root of 48

$\sqrt{147} - \sqrt{48}$

Step 1

Simplify each term.

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

Factor $49$ out of $147$ .

$\sqrt{49 (3)} - \sqrt{48}$

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

$\sqrt{7^{2} \cdot 3} - \sqrt{48}$

$\sqrt{7^{2} \cdot 3} - \sqrt{48}$

Pull terms out from under the radical.

$7 \sqrt{3} - \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$7 \sqrt{3} - \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$7 \sqrt{3} - \sqrt{4^{2} \cdot 3}$

$7 \sqrt{3} - \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$7 \sqrt{3} - (4 \sqrt{3})$

Multiply $4$ by $- 1$ .

$7 \sqrt{3} - 4 \sqrt{3}$

$7 \sqrt{3} - 4 \sqrt{3}$

Step 2

Subtract $4 \sqrt{3}$ from $7 \sqrt{3}$ .

$3 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{3}$

Decimal Form:

$5.19615242 \dots$

Related Questions