Simplify square root of 810+ square root of 240- square root of 250

$\sqrt{810} + \sqrt{240} - \sqrt{250}$

Step 1

Simplify each term.

Rewrite $810$ as $9^{2} \cdot 10$ .

Factor $81$ out of $810$ .

$\sqrt{81 (10)} + \sqrt{240} - \sqrt{250}$

Rewrite $81$ as $9^{2}$ .

$\sqrt{9^{2} \cdot 10} + \sqrt{240} - \sqrt{250}$

Pull terms out from under the radical.

$9 \sqrt{10} + \sqrt{240} - \sqrt{250}$

Rewrite $240$ as $4^{2} \cdot 15$ .

Factor $16$ out of $240$ .

$9 \sqrt{10} + \sqrt{16 (15)} - \sqrt{250}$

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

$9 \sqrt{10} + \sqrt{4^{2} \cdot 15} - \sqrt{250}$

Pull terms out from under the radical.

$9 \sqrt{10} + 4 \sqrt{15} - \sqrt{250}$

Rewrite $250$ as $5^{2} \cdot 10$ .

Factor $25$ out of $250$ .

$9 \sqrt{10} + 4 \sqrt{15} - \sqrt{25 (10)}$

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

$9 \sqrt{10} + 4 \sqrt{15} - \sqrt{5^{2} \cdot 10}$

Pull terms out from under the radical.

$9 \sqrt{10} + 4 \sqrt{15} - (5 \sqrt{10})$

Multiply $5$ by $- 1$ .

$9 \sqrt{10} + 4 \sqrt{15} - 5 \sqrt{10}$

Step 2

Subtract $5 \sqrt{10}$ from $9 \sqrt{10}$ .

$4 \sqrt{10} + 4 \sqrt{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{10} + 4 \sqrt{15}$

Decimal Form:

$28.14104402 \dots$