Simplify (5+ square root of -3)(5- square root of -3)

$(5 + \sqrt{- 3}) (5 - \sqrt{- 3})$

Rewrite $- 3$ as $- 1 (3)$ .

$(5 + \sqrt{- 1 (3)}) (5 - \sqrt{- 3})$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$(5 + \sqrt{- 1} \cdot \sqrt{3}) (5 - \sqrt{- 3})$

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

$(5 + i \cdot \sqrt{3}) (5 - \sqrt{- 3})$

Rewrite $- 3$ as $- 1 (3)$ .

$(5 + i \cdot \sqrt{3}) (5 - \sqrt{- 1 (3)})$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$(5 + i \cdot \sqrt{3}) (5 - (\sqrt{- 1} \cdot \sqrt{3}))$

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

$(5 + i \cdot \sqrt{3}) (5 - (i \cdot \sqrt{3}))$

Remove parentheses.

$(5 + i \sqrt{3}) (5 - i \sqrt{3})$

Expand $(5 + i \sqrt{3}) (5 - i \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$5 (5 - i \sqrt{3}) + i \sqrt{3} (5 - i \sqrt{3})$

Apply the distributive property.

$5 \cdot 5 + 5 (- i \sqrt{3}) + i \sqrt{3} (5 - i \sqrt{3})$

Apply the distributive property.

$5 \cdot 5 + 5 (- i \sqrt{3}) + i \sqrt{3} \cdot 5 + i \sqrt{3} (- i \sqrt{3})$

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 (- i \sqrt{3}) + i \sqrt{3} \cdot 5 + i \sqrt{3} (- i \sqrt{3})$

Multiply $- 1$ by $5$ .

$25 - 5 (i \sqrt{3}) + i \sqrt{3} \cdot 5 + i \sqrt{3} (- i \sqrt{3})$

Move $5$ to the left of $i \sqrt{3}$ .

$25 - 5 i \sqrt{3} + 5 \cdot (i \sqrt{3}) + i \sqrt{3} (- i \sqrt{3})$

Multiply $i \sqrt{3} (- i \sqrt{3})$ .

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + \sqrt{3} (- (i^{1} i) \sqrt{3})$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + \sqrt{3} (- (i^{1} i^{1}) \sqrt{3})$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + \sqrt{3} (- i^{1 + 1} \sqrt{3})$

Add $1$ and $1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + \sqrt{3} (- i^{2} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} - i^{2} ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} - i^{2} ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} - i^{2} {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} - i^{2} {\sqrt{3}}^{2}$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} - - 1 {\sqrt{3}}^{2}$

Multiply $- 1$ by $- 1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 1 {\sqrt{3}}^{2}$

Multiply ${\sqrt{3}}^{2}$ by $1$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + {(3^{\frac{1}{2}})}^{2}$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 3^{\frac{1}{2} \cdot 2}$

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

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 3^{\frac{2}{2}}$

Rewrite the expression.

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 3^{1}$

Evaluate the exponent.

$25 - 5 i \sqrt{3} + 5 i \sqrt{3} + 3$

Add $25$ and $3$ .

$- 5 i \sqrt{3} + 5 i \sqrt{3} + 28$

Add $- 5 i \sqrt{3}$ and $5 i \sqrt{3}$ .

$0 + 28$

Add $0$ and $28$ .

$28$

Simplify (5+ square root of -3)(5- square root of -3)

Related Questions

Support LCMGCF.com by disabling your adblocker.