근호의 곱셈과 유리화Multiplying Radicals & Rationalizing · 문제집Worksheet

계산하라: $\sqrt3 \times \sqrt{12}$

Compute: $\sqrt3 \times \sqrt{12}$

전개하라: $\sqrt2(\sqrt8 + \sqrt2)$

Expand: $\sqrt2(\sqrt8 + \sqrt2)$

유리화하라: $\dfrac{6}{\sqrt3}$

Rationalize: $\dfrac{6}{\sqrt3}$

계산하라: $(\sqrt5 + \sqrt2)(\sqrt5 - \sqrt2)$

Compute: $(\sqrt5 + \sqrt2)(\sqrt5 - \sqrt2)$

전개하고 간단히 하라: $(3 + \sqrt2)^2$

Expand and simplify: $(3 + \sqrt2)^2$

전개하고 간단히 하라: $(2\sqrt3 - 1)(\sqrt3 + 2)$

Expand and simplify: $(2\sqrt3 - 1)(\sqrt3 + 2)$

간단히 하라: $\dfrac{10}{\sqrt5} + \sqrt5$

Simplify: $\dfrac{10}{\sqrt5} + \sqrt5$

유리화하라: $\dfrac{1}{\sqrt6 + \sqrt5}$

Rationalize: $\dfrac{1}{\sqrt6 + \sqrt5}$

유리화하라: $\dfrac{8}{\sqrt7 - \sqrt3}$

Rationalize: $\dfrac{8}{\sqrt7 - \sqrt3}$

$x = 1 + \sqrt2$일 때 $x^2 - 2x - 1$의 값을 구하고, 그 결과가 무엇을 뜻하는지 한 문장으로 말하라.

For $x = 1 + \sqrt2$, evaluate $x^2 - 2x - 1$, and say in one sentence what the result means.

계산하라:

Evaluate:

$a = 3 + \sqrt5$, $b = 3 - \sqrt5$일 때, $a^2 + b^2$과 $\dfrac{a}{b} + \dfrac{b}{a}$의 값을 구하라.

For $a = 3 + \sqrt5$ and $b = 3 - \sqrt5$, find $a^2 + b^2$ and $\dfrac{a}{b} + \dfrac{b}{a}$.

$\sqrt{7 + 4\sqrt3}$을 $a + b\sqrt3$ ($a$, $b$는 자연수) 꼴로 나타내라.

Express $\sqrt{7 + 4\sqrt3}$ in the form $a + b\sqrt3$ with natural numbers $a$, $b$.