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Worksheets

12-1, 12-2 LC

Total questions: 15

Worksheet time: 2hrs 50mins

Name
Class
Date
1.

Simplify: 864x134-8\sqrt[4]{64x^{13}}

a)

12x134-12\sqrt[4]{x^{13}}

b)

64x3x4-64x^3\sqrt[4]{x}

c)

16x34x4-16x^3\sqrt[4]{4x}

d)

16x134-16\sqrt[4]{x^{13}}

2.

Simplify: 1283\sqrt[3]{128}

a)

2432\sqrt[3]{4}

b)

21632\sqrt[3]{16}

c)

4234\sqrt[3]{2}

d)

Cannot be simplified

3.

Simplify: 4n340m2p3\sqrt[3]{\frac{4n^3}{40m^2p}}

a)

n4325m2p3\frac{n\sqrt[3]{4}}{2\sqrt[3]{5m^2p}}

b)

n100mp2310mp\frac{n\sqrt[3]{100mp^2}}{10mp}

c)

n20mp310mp\frac{n\sqrt[3]{20mp}}{10mp}

d)

Cannot be simplified

4.

Simplify: (322752)(32422)\left(3\sqrt[2]{2}-7\sqrt[2]{5}\right)\left(\sqrt[2]{3}-4\sqrt[2]{2}\right)

a)

31621242715231\sqrt[2]{6}-12\sqrt[2]{4}-7\sqrt[2]{15}

b)

362+14102243\sqrt[2]{6}+14\sqrt[2]{10}-24

c)

352782+2872243\sqrt[2]{5}-7\sqrt[2]{8}+28\sqrt[2]{7}-24

d)

3627152+28102243\sqrt[2]{6}-7\sqrt[2]{15}+28\sqrt[2]{10}-24

5.

Simplify: (x23y16)×(x32y23)\left(x^{\frac{2}{3}}y^{\frac{1}{6}}\right)\times\left(x^{\frac{3}{2}}y^{\frac{2}{3}}\right)

a)

x2xy56x^2\sqrt[6]{xy^5}

b)

x2x6y1518x^2\sqrt[6]{x}\sqrt[18]{y^{15}}

c)

x3y2x^3\sqrt[2]{y}

d)

x136y1518\sqrt[6]{x^{13}}\sqrt[18]{y^{15}}

6.

Simplify: (z2+x)124\sqrt[4]{\left(z^2+x\right)^{12}}

a)

z6x3z^6x^3

b)

(z2+x)3\left(z^2+x\right)^3

c)

x3z2x^3\sqrt[2]{z}

d)

(z2+x)2(z2+x)2\left(z^2+x\right)^2\sqrt[2]{\left(z^2+x\right)}

7.

Simplify: 1232+3272512212\sqrt[2]{3}+3\sqrt[2]{27}-5\sqrt[2]{12}

a)

193219\sqrt[2]{3}

b)

153215\sqrt[2]{3}

c)

113211\sqrt[2]{3}

d)

Cannot be simplified. Index and radicand don't match.

8.

Simplify: 81r1143\sqrt[3]{\frac{81r^{11}}{4}}

a)

3r312r234\frac{3r^3\sqrt[3]{12r^2}}{4}

b)

3r348r34\frac{3r^3\sqrt[3]{48r}}{4}

c)

3r348r234\frac{3r^3\sqrt[3]{48r^2}}{4}

d)

3r36r232\frac{3r^3\sqrt[3]{6r^2}}{2}

9.

Simplify: 332+4\frac{3}{\sqrt[2]{3}+4}

a)

332+1219\frac{3\sqrt[2]{3}+12}{19}

b)

1233213\frac{12-3\sqrt[2]{3}}{13}

c)

3321213\frac{3\sqrt[2]{3}-12}{13}

d)

3323+432\frac{3\sqrt[2]{3}}{3+4\sqrt[2]{3}}

10.

Write using a rational exponent: x35\sqrt[5]{x^3}  

a)

x53x^{\frac{5}{3}}  

b)

x35x^{\frac{3}{5}}  

c)

x2x^2  

d)

x8x^8  

11.

Write the expression in radical form: x34x^{\frac{3}{4}}  

a)

x34\sqrt[4]{x^3}  

b)

x43\sqrt[3]{x^4}  

c)

x.75x^{.75}  

d)

x2\sqrt[]{x^2}  

12.
Rewrite the expression without using a radical:
a)

(2x+1)34\left(2x+1\right)^{\frac{3}{4}}  

b)

(2x+1)43\left(2x+1\right)^{\frac{4}{3}}  

c)

4(2x+1)34\left(2x+1\right)^3  

d)

3(2x+1)43\left(2x+1\right)^4  

13.
a)
A
b)
B
c)
C
d)
D
14.
a)
A
b)
B
c)
C
d)
D
15.
a)
a
b)
b
c)
c
d)
d