Simplifying radicals

This topic contains 2 replies, has 3 voices, and was last updated by  Bill McCallum 3 years, 7 months ago.

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  • #3037

    bbaggett
    Participant

    8.NS.2 asks students to use rational approximations of irrational numbers to compare the size of irrationsal numbers, locat them on a number line diagram and estimate the value of expressions. 8.EE.2 says to use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p and to evaluate tje square roots of small perfect squares and cube roots of small perfect cubes.

    So….this does not look to me like 8th grade students should be simplifying radicals since 8th grade is the first time students have worked with square roots and cube roots (and the standards say specifically perfect squares and perfect cubes). But, I don’t see anything in the high school standards that says where simplifying radicals should be taught. My Algebra I teachers believe it should be in 8th grade. My 8th grade teachers believe it should be in Algebra I. What was the intention?

    #3039

    Alexei Kassymov
    Participant

    Expressions and Equations progression says: “Notice that students do not learn the properties of rational exponents until high school.” (a*b)^(1/2) = a^(1/2)*b^(1/2) in the form sqrt(a*b)=sqrt(a)*sqrt(b) appears to fit this description.

    On the other hand N-RN.2 looks very appropriate. Part b in the task below uses the property:
    https://www.illustrativemathematics.org/illustrations/608

    Algebra I makes more sense.

    #3058

    Bill McCallum
    Keymaster

    Simplifying radicals is one of those high school topics that has evolved into a cancerous growth on the curriculum, starving other more important topics for resources. What is important is for students to understand and use the laws of exponents. When they get to algebra they should be able to see that $\sqrt{x^2y}$ is the same as $x\sqrt{y}$ (if $x$ and $y$ are positive). Seeing that $\sqrt{45} = 3 \sqrt{5}$ is a sort of rehearsal for this, and as Alexei points out comes quite appropriately N-RN.2. But treating such simplification as an end in itself, accompanied by long lists of problems, is an example of misplaced priorities. That’s why the standards don’t make explicit mention of it.

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