Evaluate square root of 48+ square root of 75

$\sqrt{48} + \sqrt{75}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

$\sqrt{16 (3)} + \sqrt{75}$

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

$\sqrt{4^{2} \cdot 3} + \sqrt{75}$

$\sqrt{4^{2} \cdot 3} + \sqrt{75}$

Pull terms out from under the radical.

$4 \sqrt{3} + \sqrt{75}$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$4 \sqrt{3} + \sqrt{25 (3)}$

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

$4 \sqrt{3} + \sqrt{5^{2} \cdot 3}$

$4 \sqrt{3} + \sqrt{5^{2} \cdot 3}$

Pull terms out from under the radical.

$4 \sqrt{3} + 5 \sqrt{3}$

$4 \sqrt{3} + 5 \sqrt{3}$

Step 2

Add $4 \sqrt{3}$ and $5 \sqrt{3}$ .

$9 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$9 \sqrt{3}$

Decimal Form:

$15.58845726 \dots$

Related Questions