Simplify (3 square root of 5-2 square root of 3)(2+ square root of 3)

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

Step 1

Expand $(3 \sqrt{5} - 2 \sqrt{3}) (2 + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$3 \sqrt{5} \cdot 2 + 3 \sqrt{5} \sqrt{3} - 2 \sqrt{3} (2 + \sqrt{3})$

Apply the distributive property.

$3 \sqrt{5} \cdot 2 + 3 \sqrt{5} \sqrt{3} - 2 \sqrt{3} \cdot 2 - 2 \sqrt{3} \sqrt{3}$

Step 2

Simplify each term.

Multiply $2$ by $3$ .

$6 \sqrt{5} + 3 \sqrt{5} \sqrt{3} - 2 \sqrt{3} \cdot 2 - 2 \sqrt{3} \sqrt{3}$

Multiply $3 \sqrt{5} \sqrt{3}$ .

Combine using the product rule for radicals.

$6 \sqrt{5} + 3 \sqrt{3 \cdot 5} - 2 \sqrt{3} \cdot 2 - 2 \sqrt{3} \sqrt{3}$

Multiply $3$ by $5$ .

$6 \sqrt{5} + 3 \sqrt{15} - 2 \sqrt{3} \cdot 2 - 2 \sqrt{3} \sqrt{3}$

Multiply $2$ by $- 2$ .

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \sqrt{3} \sqrt{3}$

Multiply $- 2 \sqrt{3} \sqrt{3}$ .

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 ({\sqrt{3}}^{1} \sqrt{3})$

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 {\sqrt{3}}^{2}$

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

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 {(3^{\frac{1}{2}})}^{2}$

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \cdot 3^{1}$

Evaluate the exponent.

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 2 \cdot 3$

Multiply $- 2$ by $3$ .

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 6$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5} + 3 \sqrt{15} - 4 \sqrt{3} - 6$

Decimal Form:

$12.10715467 \dots$

Simplify (3 square root of 5-2 square root of 3)(2+ square root of 3)

Related Questions

Support LCMGCF.com by disabling your adblocker.