Simplifying Radical Expressions

Review Material: Simplifying numerical radical expressions

$\rhd$ Simplifying square roots (3:08) $5 \sqrt{117} = 5 \sqrt{3^2 \cdot 13} = 15 \sqrt{13}$ and $3 \sqrt{26}$ cannot be simplified.
$\rhd$ Simplifying square roots of fractions (4:40) $\sqrt{\dfrac{1}{200}} = \dfrac{1}{10\sqrt{2}} = \dfrac{\sqrt{2}}{20}$
$\star$ Simplifying square roots $\sqrt{\dfrac{1}{44}}$
$\rhd$ Simplifying sums of radicals (4:41) He uses the correct $|x| = \sqrt{x^2}$ rather than the (false) $\sqrt{x^2} = x$ . Hooray!
Solve: $\sqrt{2x^2} + 4\sqrt{8} + 3\sqrt{2x^2} + \sqrt{8} = (4|x| + 10)\sqrt{2}$
$\rhd$ Simplifying differences of radicals (5:45) $4 \sqrt[4]{81x^5} - 2\sqrt[4]{81x^5} - \sqrt{x^3} = 6|x| \sqrt[4]{x} - |x|\sqrt{x}$ In this video he correctly remarks that “If $x>0$ , there’s no need for the $|x|$ .”
$\star$ Simplifying square root expressions (with no variables) $\sqrt{\dfrac{6^2}{95}}$
$\rhd$ Introduction to rationalizing the denominator (10:17) [Example 1] $\dfrac{1}{2}$
[Example 2] $\dfrac{7}{15}$
[Example 3] $\dfrac{12}{2 - \sqrt{5}}$ Sal shows why multiplying by $\dfrac{\sqrt{5}}{\sqrt{5}}$ doesn’t help and why multiplying by $\dfrac{2+\sqrt{5}}{2+\sqrt{5}}$ does — difference of squares!
[Example 4] $\dfrac{5y}{2\sqrt{y} - 5} = \dfrac{10}{4y-25}$

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The OpenLab at City Tech:A place to learn, work, and share

The OpenLab is an open-source, digital platform designed to support teaching and learning at City Tech (New York City College of Technology), and to promote student and faculty engagement in the intellectual and social life of the college community.