근호를 포함한 식의 계산

Mixed Practice

$\left(4\sqrt{6}\right)\left(-\sqrt{18}\right)$

Mixed Practice

$\left(7\sqrt[3]{4}\right)\left(-3\sqrt[3]{18}\right)$

Mixed Practice

$\left(4\sqrt{12{x}^{5}}\right)\left(2\sqrt{6{x}^{3}}\right)$

Mixed Practice

${\left(\sqrt{29}\right)}^{2}$

Mixed Practice

$\left(-4\sqrt{17}\right)\left(-3\sqrt{17}\right)$

Mixed Practice

$\left(-4+\sqrt{17}\right)\left(-3+\sqrt{17}\right)$

Mixed Practice

$\left(3\,\sqrt[4]{8{a}^{2}}\right)\left(\sqrt[4]{12{a}^{3}}\right)$

Mixed Practice

${\left(6-3\sqrt{2}\right)}^{2}$

Mixed Practice

$\sqrt{3}\left(4-3\sqrt{3}\right)$

Mixed Practice

$\sqrt[3]{3}\,\left(2\,\sqrt[3]{9}+\sqrt[3]{18}\right)$

Mixed Practice

$\left(\sqrt{6}+\sqrt{3}\right)\left(\sqrt{6}+6\sqrt{3}\right)$

Explain when a radical expression is in simplest form.

Explain the process for determining whether two radicals are like or unlike. Make sure your answer makes sense for radicals containing both numbers and variables.

ⓐ Explain why ${\left(-\sqrt{n}\right)}^{2}$ is always non-negative, for $n\ge 0.$ ⓑ Explain why $-{\left(\sqrt{n}\right)}^{2}$ is always non-positive, for $n\ge 0.$

Use the binomial square pattern to simplify ${\left(3+\sqrt{2}\right)}^{2}.$ Explain all your steps.

Simplify: $\frac{30}{48}.$

Simplify: ${x}^{2}\cdot {x}^{4}.$

Multiply: $(7+3x)(7-3x).$

Simplify: ⓐ $\frac{\sqrt{72{x}^{3}}}{\sqrt{162x}}$ ⓑ $\frac{\sqrt[3]{32{x}^{2}}}{\sqrt[3]{4{x}^{5}}}.$

Simplify: ⓐ $\frac{\sqrt{50{s}^{3}}}{\sqrt{128s}}$ ⓑ $\frac{\sqrt[3]{56{a}^{}}}{\sqrt[3]{7{a}^{4}}}.$