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10.9: Radicals- Answers to the Homework Exercises

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    Simplify Radicals

    1. \(7\sqrt{5}\)
    1. \(2\sqrt{3}\)
    1. \(48\sqrt{2}\)
    1. \(8\sqrt{3n}\)
    1. \(6x\sqrt{7}\)
    1. \(-56x^2\)
    1. \(3xy\sqrt{5}\)
    1. \(8x^2y^2\sqrt{5}\)
    1. \(35xy\sqrt{5y}\)
    1. \(-48x^2z^2y\sqrt{5}\)
    1. \(-12p\sqrt{6mn}\)
    1. \(14\)
    1. \(20\sqrt{2}\)
    1. \(-21\sqrt{7}\)
    1. \(10n\sqrt{n}\)
    1. \(-20p^2\sqrt{7}\)
    1. \(32p\sqrt{7}\)
    1. \(16a^2b\sqrt{2}\)
    1. \(56\sqrt{2mn}\)
    1. \(-30y^2x\sqrt{2x}\)
    1. \(-4yz\sqrt{2xz}\)
    1. \((\sqrt[5]{m})^3\)
    1. \((\sqrt{7x})^3\)
    1. \((6x)^{-\dfrac{3}{2}}\)
    1. \(n^{-\dfrac{7}{4}}\)
    1. \(4\)
    1. \(8\)

    Add and Subtract Radicals

    1. \(6\sqrt{5}\)
    1. \(-5\sqrt{6}\)
    1. \(-8\sqrt{2}\)
    1. \(-2\sqrt{2}\)
    1. \(-3\sqrt{6}-\sqrt{3}\)
    1. \(-4\sqrt{6}+4\sqrt{5}\)
    1. \(2\sqrt[3]{2}\)
    1. \(\sqrt[4]{2}-3\sqrt[4]{3}\)
    1. \(2\sqrt[4]{2}+\sqrt[4]{3}+6\sqrt[4]{4}\)
    1. \(4\sqrt[5]{5}-4\sqrt[5]{6}\)
    1. \(-3\sqrt{6}-5\sqrt{3}\)
    1. \(-3\sqrt{3}\)
    1. \(-6\sqrt{6}+9\sqrt{3}\)
    1. \(8\sqrt{5}-\sqrt{3}\)
    1. \(3\sqrt{2}+3\sqrt{6}\)
    1. \(-\sqrt{5}-3\sqrt{6}\)
    1. \(6\sqrt[3]{5}-3\sqrt[3]{3}\)
    1. \(5\sqrt[4]{6}+2\sqrt[4]{4}\)
    1. \(-2\sqrt[4]{3}-9\sqrt[4]{5}-3\sqrt[4]{2}\)
    1. \(-11\sqrt[7]{2}-2\sqrt[7]{5}\)

    Multiply and Divide Radicals

    1. \(-48\sqrt{5}\)
    1. \(2x^2\sqrt[3]{x}\)
    1. \(-45\sqrt{5}-10\sqrt{15}\)
    1. \(-2-4\sqrt{2}\)
    1. \(6a+a\sqrt{10}+6a\sqrt{6}+2a\sqrt{15}\)
    1. \(\dfrac{\sqrt{3}}{25}\)
    1. \(\dfrac{\sqrt{5}}{2}\)
    1. \(\dfrac{5}{12y^4}\)
    1. \(\dfrac{\sqrt[3]{10}}{5}\)
    1. \(\dfrac{5\sqrt[4]{r^2}}{2}\) or \(\dfrac{5\sqrt{r}}{2}\)
    1. \(-25r^2\sqrt{2r}\)
    1. \(5\sqrt{2}+2\sqrt{5}\)
    1. \(5\sqrt{3}-9\sqrt{5v}\)
    1. \(30+8\sqrt{3}+5\sqrt{15}+4\sqrt{5}\)
    1. \(-10\sqrt{m}+25\sqrt{2}+\sqrt{2m}-5\)
    1. \(2\)
    1. \(4\sqrt{2}\)
    1. \(\dfrac{\sqrt{n}}{2}\)
    1. \(\dfrac{1}{4}\)

    Rationalize Denominators

    1. \(\dfrac{4\sqrt{3}}{9}\)
    1. \(2\)
    1. \(\dfrac{4\sqrt{5}}{5}\)
    1. \(\dfrac{2+\sqrt{3}}{5}\)
    1. \(\dfrac{\sqrt{6}-9}{3}\)
    1. \(\dfrac{10-2\sqrt{2}}{23}\)
    1. \(3-\sqrt{5}\)
    1. \(\sqrt{2}-1\)
    1. \(\sqrt{a}\)
    1. \(4-2\sqrt{3}+2\sqrt{6}-3\sqrt{2}\)
    1. \(3\sqrt{2}+2\sqrt{3}\)
    1. \(\dfrac{-1+\sqrt{5}}{4}\)
    1. \(\dfrac{\sqrt{3}-1}{4}\)
    1. \(\dfrac{\sqrt{30}-2\sqrt{3}}{18}\)
    1. \(\dfrac{2\sqrt{3}+\sqrt{2}}{2}\)
    1. \(\dfrac{\sqrt{5}-\sqrt{3}}{2}\)
    1. \(3+2\sqrt{3}\)
    1. \(3-2\sqrt{2}\)
    1. \(\dfrac{2\sqrt{5}-2\sqrt{15}+\sqrt{3}+3}{-2}\)
    1. \(\dfrac{a\sqrt{b}+b\sqrt{a}}{a-b}\)
    1. \(\dfrac{2\sqrt{5}-5\sqrt{2}-10+5\sqrt{10}}{30}\)
    1. \(\dfrac{8+3\sqrt{6}}{10}\)

    Radicals with Mixed Indices

    1. \(\sqrt[4]{4x^2y^3}\)
    1. \(\dfrac{\sqrt[3]{36xy}}{3y}\)
    1. \(\sqrt[4]{x^3y^2z}\)
    1. \(\sqrt{3xy^3}\)
    1. \(\sqrt[5]{x^3y^4z^2}\)
    1. \(\sqrt{5y}\)
    1. \(\sqrt[6]{5400}\)
    1. \(\sqrt[6]{x^3(x-2)^2}\)
    1. \(\sqrt[12]{x^{11}y^{10}}\)
    1. \(a\sqrt[4]{a}\)
    1. \(xy\sqrt[6]{xy^5}\)
    1. \(x\sqrt[12]{59049xy^{11}z^{10}}\)
    1. \(\sqrt[12]{a^5}\)
    1. \(\sqrt[10]{ab^9c^7}\)
    1. \(\sqrt[15]{(2x+1)^4}\)
    1. \(\sqrt[15]{27y^5z^5}\)
    1. \(\sqrt[10]{4a^9b^9}\)
    1. \(\sqrt[30]{x^{22}y^{11}z^{27}}\)
    1. \(a\sqrt[12]{a^5}\)
    1. \(2xy^2\sqrt[6]{2x^5y}\)
    1. \(4x(y+z)^3\sqrt[6]{2x(y+z)}\)
    1. \(\dfrac{\sqrt[15]{a^7b^{11}}}{b}\)
    1. \(\sqrt[12]{(2+5x)^5}\)

    Radical Equations

    1. \(3\)
    1. \(\pm 2\)
    1. \(5\)
    1. \(5\)
    1. \(3\)
    1. \(3\)
    1. \(7\)
    1. \(21\)
      1. \(79.5\) inches
      2. \(145.7\) pounds

    Solving with Rational Exponents

    1. \(\pm 5\sqrt{3}\)
    1. \(\pm 2\sqrt{6}\)
    1. \(-1\)
    1. \(-7\)
    1. \(-\dfrac{3}{8}, -\dfrac{5}{8}\)
    1. \(-\dfrac{34}{3}, -10\)
    1. \(-2\)
    1. \(-3,11\)
    1. \(\dfrac{-1\pm 3\sqrt{2}}{2}\)
    1. \(-\dfrac{11}{2},\dfrac{5}{2}\)
    1. \(\dfrac{9}{8}\)
    1. \(3\)

    Complex Numbers

    1. \(8i\)
    1. \(9i\)
    1. \(10i\)
    1. \(3i\sqrt{10}\)
    1. \(7i\sqrt{5}\)
    1. \(40\)
    1. \(-12\)
    1. \(-15\)
    1. \(-2\sqrt{5}\)
    1. \(-7-4i\)
    1. \(2-5i\)
    1. \(\dfrac{1+i\sqrt{3}}{2}\)
    1. \(\dfrac{2+i\sqrt{2}}{2}\)
    1. \(5-i\sqrt{3}\)
    1. \(\dfrac{5+2i\sqrt{3}}{2}\)
    1. \(11-4i\)
    1. \(-3-13i\)
    1. \(-8-2i\)
    1. \(80-10i\)
    1. \(44+8i\)
    1. \(9i+5\)
    1. \(\dfrac{3i-6}{4}\)
    1. \(\dfrac{-40i+4}{101}\)
    1. \(\dfrac{70+49i}{149}\)
    1. \(-4i\)
    1. \(5-12i\)
    1. \(13-8i\)
    1. \(-32-128i\)
    1. \(-28+76i\)
    1. \(-1+13i\)
    1. \(\dfrac{4i+2}{3}\)
    1. \(-2i\)
    1. \(\dfrac{4-6i}{13}\)
    1. \(\dfrac{48i-56}{85}\)
    1. \(1\)
    1. \(-1\)
    1. \(1\)
    1. \(-i\)

    This page titled 10.9: Radicals- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform.