Evaluate (4+ square root of 5)^2

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

Rewrite ${(4 + \sqrt{5})}^{2}$ as $(4 + \sqrt{5}) (4 + \sqrt{5})$ .

$(4 + \sqrt{5}) (4 + \sqrt{5})$

Expand $(4 + \sqrt{5}) (4 + \sqrt{5})$ using the FOIL Method.

Tap for more steps…

Apply the distributive property.

$4 (4 + \sqrt{5}) + \sqrt{5} (4 + \sqrt{5})$

Apply the distributive property.

$4 \cdot 4 + 4 \sqrt{5} + \sqrt{5} (4 + \sqrt{5})$

Apply the distributive property.

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

Simplify and combine like terms.

Tap for more steps…

Simplify each term.

Tap for more steps…

Multiply $4$ by $4$ .

$16 + 4 \sqrt{5} + \sqrt{5} \cdot 4 + \sqrt{5} \sqrt{5}$

Move $4$ to the left of $\sqrt{5}$ .

$16 + 4 \sqrt{5} + 4 \cdot \sqrt{5} + \sqrt{5} \sqrt{5}$

Combine using the product rule for radicals.

$16 + 4 \sqrt{5} + 4 \sqrt{5} + \sqrt{5 \cdot 5}$

Multiply $5$ by $5$ .

$16 + 4 \sqrt{5} + 4 \sqrt{5} + \sqrt{25}$

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

$16 + 4 \sqrt{5} + 4 \sqrt{5} + \sqrt{5^{2}}$

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

$16 + 4 \sqrt{5} + 4 \sqrt{5} + 5$

Add $16$ and $5$ .

$21 + 4 \sqrt{5} + 4 \sqrt{5}$

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

$21 + 8 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$21 + 8 \sqrt{5}$

Decimal Form:

$38.88854381 \dots$

Evaluate (4+ square root of 5)^2

Download our
App from the store