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Worksheets6.1 & 6.2 Rational Exponents and Radicals
Total questions: 10
Worksheet time: 15mins
Find the indicated real nth root(s) of a.
n = 5 , a = -243
3
-3
±3
no real roots
Find the indicated real nth root(s) of a.
n = 8 , a = 256
2
-2
±2
no real roots
Find the real solution(s) of 5x3 = 320.
4
±4
8
±8
Find the real solution(s) of (x + 3)4 = 24.
x ≈ 2.14
x ≈ 2.14 or x ≈ -2.14
x ≈ - 0.79 or x ≈ -5.21
x ≈ - 0.79
Find the radius, given V = 4/3 π r3
7.18 ft
6.00 ft
4.51 ft
3.72 ft
An expression containing a radical with index n is in simplest form when these three conditions are met.
No radicands have perfect nth powers as factors.
No radicands contain negative numbers.
No radicands contain fractions.
No radicals appear in the numerator of a fraction.
No radicals appear in the denominator of a fraction.
Write in simplest form. ∛500
167 ⅔
5 ∛4
10 √5
3 ∛167
Identify the conjugate of a√b + c√d
a√b + c√d
a√b - c√d
√b - √d
√b + √d
To rationalize a denominator of 2 - √7
multiply the numerator and denominator by √7
multiply the denominator by 2 + √7
multiply the numerator and denominator by 2 - √7
multiply the numerator and denominator by 2 + √7
multiply the denominator by √7
Simplify ∛(27d12)
9d4
3d4
3d9
9d9
