Finite Math Examples

$(\sqrt{4 + \sqrt{25}}) (\sqrt{16 - \sqrt{49}})$

Step 1

Combine using the product rule for radicals.

$\sqrt{(4 + \sqrt{25}) (16 - \sqrt{49})}$

Step 2

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

$\sqrt{(4 + \sqrt{5^{2}}) (16 - \sqrt{49})}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{(4 + 5) (16 - \sqrt{49})}$

Step 4

Add $4$ and $5$ .

$\sqrt{9 (16 - \sqrt{49})}$

Step 5

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

$\sqrt{9 (16 - \sqrt{7^{2}})}$

Step 6

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt{9 (16 - 1 \cdot 7)}$

Step 7

Multiply $- 1$ by $7$ .

$\sqrt{9 (16 - 7)}$

Step 8

Subtract $7$ from $16$ .

$\sqrt{9 \cdot 9}$

Step 9

Multiply $9$ by $9$ .

$\sqrt{81}$

Step 10

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

$\sqrt{9^{2}}$

Step 11

Pull terms out from under the radical, assuming positive real numbers.

$9$