Simplify (4+ square root of z)( square root of 11+ square root of z)

$(4 + \sqrt{z}) (\sqrt{11} + \sqrt{z})$

Step 1

Expand $(4 + \sqrt{z}) (\sqrt{11} + \sqrt{z})$ using the FOIL Method.

Apply the distributive property.

$4 (\sqrt{11} + \sqrt{z}) + \sqrt{z} (\sqrt{11} + \sqrt{z})$

Apply the distributive property.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z} (\sqrt{11} + \sqrt{z})$

Apply the distributive property.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z} \sqrt{11} + \sqrt{z} \sqrt{z}$

Step 2

Simplify terms.

Simplify each term.

Combine using the product rule for radicals.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + \sqrt{z} \sqrt{z}$

Multiply $\sqrt{z} \sqrt{z}$ .

Raise $\sqrt{z}$ to the power of $1$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + {\sqrt{z}}^{1} \sqrt{z}$

Raise $\sqrt{z}$ to the power of $1$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + {\sqrt{z}}^{1} {\sqrt{z}}^{1}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + {\sqrt{z}}^{1 + 1}$

Add $1$ and $1$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + {\sqrt{z}}^{2}$

Rewrite ${\sqrt{z}}^{2}$ as $z$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{z}$ as $z^{\frac{1}{2}}$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + {(z^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z^{\frac{2}{2}}$

Rewrite the expression.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z^{1}$

Simplify.

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z$

Simplify the expression.

Reorder factors in $4 \sqrt{11} + 4 \sqrt{z} + \sqrt{z \cdot 11} + z$ .

$4 \sqrt{11} + 4 \sqrt{z} + \sqrt{11 z} + z$

Move $\sqrt{11 z}$ .

$4 \sqrt{11} + 4 \sqrt{z} + z + \sqrt{11 z}$

Move $4 \sqrt{z}$ .

$4 \sqrt{11} + z + 4 \sqrt{z} + \sqrt{11 z}$

Reorder $4 \sqrt{11}$ and $z$ .

$z + 4 \sqrt{11} + 4 \sqrt{z} + \sqrt{11 z}$

Simplify (4+ square root of z)( square root of 11+ square root of z)

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