1
\tfrac{2}{21}
Chapter 21 · Square Root and Radicals
Chapter challenge
Ten problems drawn from every lesson in the chapter. Get each one right on your first try for a perfect score. A new set is drawn each time.
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From Square Root of Numbers, exercise 12
Extract the square root, correct to three decimal places, of:
From Square Root of Polynomials, exercise 17
Extract the square root of:
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\dfrac{9}{4} - \dfrac{127 m^{2}}{18} + \dfrac{25 m^{4}}{4} - 2 m + \dfrac{10 m^{3}}{3}
From Radicals and Fractional Exponents, exercise 35
Find the numerical values of:
3
\sqrt[3]{8^2}\cdot 25^{3/2}
From Addition and Subtraction of Radicals, exercise 11
Simplify and collect:
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\sqrt{\tfrac5{18}} + 2\sqrt{\tfrac{32}5} - \sqrt{\tfrac{10}9}
From Factors Involving Radicals, exercise 1
Factor:
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x^{2} - 6
From Multiplication of Radicals, exercise 16
Perform the indicated multiplications and simplify the products:
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\sqrt{\dfrac ax}\cdot\sqrt{\dfrac{4x}a}
From Radicals of Different Orders; Products of Polynomials, exercise 38
Perform the indicated multiplications and simplify the products:
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\left(3\sqrt2 + 2\sqrt3 + \sqrt{30}\right)\left(\sqrt2 + \sqrt3 - \sqrt5\right)
From More Simplification; Radicals Under One Sign, exercise 54
Express entirely under the radical sign:
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2x^2\sqrt[3]{x^2}
From Problems in Simplest Radical Form, exercise 14
Obtain answers in simplest radical form.
9
The legs of a right triangle are R and \dfrac R2\left(\sqrt5 - 1\right). Find the hypotenuse.
From Rationalizing Factors, exercise 15
Determine a rationalizing factor for each of the following expressions and find the product of the expression and the factor:
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\sqrt3 - \sqrt2