Question

Perform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)

Accepted Answer

Identify the expression to be simplified: $$ (3\sqrt{2} + \sqrt{3})(2\sqrt{3} - \sqrt{2}) . $$This is a product of two binomials involving square roots. Apply the distributive property (FOIL method) to multiply each term in the first binomial by each term in the second binomial:

$$ (3\sqrt{2})(2\sqrt{3}) + (3\sqrt{2})(-\sqrt{2}) + (\sqrt{3})(2\sqrt{3}) + (\sqrt{3})(-\sqrt{2}) $$ Simplify each product by multiplying the coefficients and the square roots separately, remembering that $$ \sqrt{a} 	imes \sqrt{b} = \sqrt{ab} $$:

- $$ 3 	imes 2 = 6 $$ and $$ \sqrt{2} 	imes \sqrt{3} = \sqrt{6} $$
- $$ 3 	imes (-1) = -3 $$ and $$ \sqrt{2} 	imes \sqrt{2} = \sqrt{4} $$
- $$ 1 	imes 2 = 2 $$ and $$ \sqrt{3} 	imes \sqrt{3} = \sqrt{9} $$
- $$ 1 	imes (-1) = -1 $$ and $$ \sqrt{3} 	imes \sqrt{2} = \sqrt{6} $$ Rewrite the expression with the simplified terms:

$$ 6\sqrt{6} - 3\sqrt{4} + 2\sqrt{9} - \sqrt{6} $$ Simplify the square roots of perfect squares ($$ \sqrt{4} = 2 $$, $$ \sqrt{9} = 3 $$), then combine like terms (terms with $$ \sqrt{6} ) to $$write the expression in its simplest form.

Perform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Operations with Radicals

Distributive Property

Simplifying Radicals