Pre-Algebra Examples

${(9 + \sqrt{7})}^{2}$

Step 1

Rewrite ${(9 + \sqrt{7})}^{2}$ as $(9 + \sqrt{7}) (9 + \sqrt{7})$ .

$(9 + \sqrt{7}) (9 + \sqrt{7})$

Step 2

Expand $(9 + \sqrt{7}) (9 + \sqrt{7})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$9 (9 + \sqrt{7}) + \sqrt{7} (9 + \sqrt{7})$

Step 2.2

Apply the distributive property.

$9 \cdot 9 + 9 \sqrt{7} + \sqrt{7} (9 + \sqrt{7})$

Step 2.3

Apply the distributive property.

$9 \cdot 9 + 9 \sqrt{7} + \sqrt{7} \cdot 9 + \sqrt{7} \sqrt{7}$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $9$ by $9$ .

$81 + 9 \sqrt{7} + \sqrt{7} \cdot 9 + \sqrt{7} \sqrt{7}$

Step 3.1.2

Move $9$ to the left of $\sqrt{7}$ .

$81 + 9 \sqrt{7} + 9 \cdot \sqrt{7} + \sqrt{7} \sqrt{7}$

Step 3.1.3

Combine using the product rule for radicals.

$81 + 9 \sqrt{7} + 9 \sqrt{7} + \sqrt{7 \cdot 7}$

Step 3.1.4

Multiply $7$ by $7$ .

$81 + 9 \sqrt{7} + 9 \sqrt{7} + \sqrt{49}$

Step 3.1.5

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

$81 + 9 \sqrt{7} + 9 \sqrt{7} + \sqrt{7^{2}}$

Step 3.1.6

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

$81 + 9 \sqrt{7} + 9 \sqrt{7} + 7$

Step 3.2

Add $81$ and $7$ .

$88 + 9 \sqrt{7} + 9 \sqrt{7}$

Step 3.3

Add $9 \sqrt{7}$ and $9 \sqrt{7}$ .

$88 + 18 \sqrt{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$88 + 18 \sqrt{7}$

Decimal Form:

$135.62352359 \dots$