Simplify (14+ square root of -52)(12+ square root of -208)

$(14 + \sqrt{- 52}) (12 + \sqrt{- 208})$

Rewrite $- 52$ as $- 1 (52)$ .

$(14 + \sqrt{- 1 (52)}) (12 + \sqrt{- 208})$

Rewrite $\sqrt{- 1 (52)}$ as $\sqrt{- 1} \cdot \sqrt{52}$ .

$(14 + \sqrt{- 1} \cdot \sqrt{52}) (12 + \sqrt{- 208})$

Rewrite $\sqrt{- 1}$ as $i$ .

$(14 + i \cdot \sqrt{52}) (12 + \sqrt{- 208})$

Rewrite $- 208$ as $- 1 (208)$ .

$(14 + i \cdot \sqrt{52}) (12 + \sqrt{- 1 (208)})$

Rewrite $\sqrt{- 1 (208)}$ as $\sqrt{- 1} \cdot \sqrt{208}$ .

$(14 + i \cdot \sqrt{52}) (12 + \sqrt{- 1} \cdot \sqrt{208})$

Rewrite $\sqrt{- 1}$ as $i$ .

$(14 + i \cdot \sqrt{52}) (12 + i \cdot \sqrt{208})$

Simplify terms.

Simplify each term.

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$(14 + i \cdot \sqrt{4 (13)}) (12 + i \cdot \sqrt{208})$

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

$(14 + i \cdot \sqrt{2^{2} \cdot 13}) (12 + i \cdot \sqrt{208})$

Pull terms out from under the radical.

$(14 + i \cdot (2 \sqrt{13})) (12 + i \cdot \sqrt{208})$

Move $2$ to the left of $i$ .

$(14 + 2 i \sqrt{13}) (12 + i \cdot \sqrt{208})$

Simplify each term.

Rewrite $208$ as $4^{2} \cdot 13$ .

Factor $16$ out of $208$ .

$(14 + 2 i \sqrt{13}) (12 + i \cdot \sqrt{16 (13)})$

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

$(14 + 2 i \sqrt{13}) (12 + i \cdot \sqrt{4^{2} \cdot 13})$

Pull terms out from under the radical.

$(14 + 2 i \sqrt{13}) (12 + i \cdot (4 \sqrt{13}))$

Move $4$ to the left of $i$ .

$(14 + 2 i \sqrt{13}) (12 + 4 i \sqrt{13})$

Expand $(14 + 2 i \sqrt{13}) (12 + 4 i \sqrt{13})$ using the FOIL Method.

Apply the distributive property.

$14 (12 + 4 i \sqrt{13}) + 2 i \sqrt{13} (12 + 4 i \sqrt{13})$

Apply the distributive property.

$14 \cdot 12 + 14 (4 i \sqrt{13}) + 2 i \sqrt{13} (12 + 4 i \sqrt{13})$

Apply the distributive property.

$14 \cdot 12 + 14 (4 i \sqrt{13}) + 2 i \sqrt{13} \cdot 12 + 2 i \sqrt{13} (4 i \sqrt{13})$

Simplify and combine like terms.

Simplify each term.

Multiply $14$ by $12$ .

$168 + 14 (4 i \sqrt{13}) + 2 i \sqrt{13} \cdot 12 + 2 i \sqrt{13} (4 i \sqrt{13})$

Multiply $4$ by $14$ .

$168 + 56 (i \sqrt{13}) + 2 i \sqrt{13} \cdot 12 + 2 i \sqrt{13} (4 i \sqrt{13})$

Multiply $12$ by $2$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 2 i \sqrt{13} (4 i \sqrt{13})$

Multiply $2 i \sqrt{13} (4 i \sqrt{13})$ .

Multiply $4$ by $2$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i \sqrt{13} (i \sqrt{13})$

Raise $i$ to the power of $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 (i^{1} i) \sqrt{13} \sqrt{13}$

Raise $i$ to the power of $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 (i^{1} i^{1}) \sqrt{13} \sqrt{13}$

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

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{1 + 1} \sqrt{13} \sqrt{13}$

Add $1$ and $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{2} \sqrt{13} \sqrt{13}$

Raise $\sqrt{13}$ to the power of $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{2} ({\sqrt{13}}^{1} \sqrt{13})$

Raise $\sqrt{13}$ to the power of $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{2} ({\sqrt{13}}^{1} {\sqrt{13}}^{1})$

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

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{2} {\sqrt{13}}^{1 + 1}$

Add $1$ and $1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 i^{2} {\sqrt{13}}^{2}$

Rewrite $i^{2}$ as $- 1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} + 8 \cdot - 1 {\sqrt{13}}^{2}$

Multiply $8$ by $- 1$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 {\sqrt{13}}^{2}$

Rewrite ${\sqrt{13}}^{2}$ as $13$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{13}$ as $13^{\frac{1}{2}}$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 {(13^{\frac{1}{2}})}^{2}$

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

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 \cdot 13^{\frac{1}{2} \cdot 2}$

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

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 \cdot 13^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 \cdot 13^{\frac{2}{2}}$

Rewrite the expression.

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 \cdot 13^{1}$

Evaluate the exponent.

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 8 \cdot 13$

Multiply $- 8$ by $13$ .

$168 + 56 i \sqrt{13} + 24 i \sqrt{13} - 104$

Subtract $104$ from $168$ .

$56 i \sqrt{13} + 24 i \sqrt{13} + 64$

Add $56 i \sqrt{13}$ and $24 i \sqrt{13}$ .

$80 i \sqrt{13} + 64$

Reorder $80 i \sqrt{13}$ and $64$ .

$64 + 80 i \sqrt{13}$

Simplify (14+ square root of -52)(12+ square root of -208)

Related Questions

Support LCMGCF.com by disabling your adblocker.