Chapter 2. Exponents and Radicals
Chapter 2. Exponents and Radicals
Chapter 2. Exponents and Radicals
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MODULE - 1<br />
Algebra<br />
<strong>Exponents</strong> <strong>and</strong> <strong>Radicals</strong><br />
Notes<br />
⎛ 37 ⎞<br />
(ii) ⎜ − ⎟<br />
⎝ 19 ⎠<br />
(iii)<br />
⎡⎛<br />
⎢⎜<br />
⎢⎣<br />
⎝<br />
3<br />
13<br />
20<br />
⎛ 37 ⎞ ÷ ⎜ − ⎟<br />
⎝ 19 ⎠<br />
5<br />
3<br />
⎞ ⎤<br />
⎟ ⎥<br />
⎠ ⎥⎦<br />
4. Simplify each of the following:<br />
(i) 3 o + 7 o + 37 o – 3 (ii) ( 7 o + 3 o ) ( 7 o – 3 o )<br />
5. Simplify the following:<br />
20<br />
(i) ( ) 12 −<br />
32 ÷ ( 32) 6 (ii) ( ) 6 −<br />
111 ( 111) 5<br />
⎛ 3 ⎞<br />
6. Find x so that ⎜ ⎟<br />
⎝ 7 ⎠<br />
⎛ 3<br />
7. Find x so that ⎜<br />
⎝13<br />
−3<br />
⎞<br />
⎟<br />
⎠<br />
⎛ 3 ⎞<br />
× ⎜ ⎟<br />
⎝ 7 ⎠<br />
−2<br />
⎛<br />
× ⎜<br />
⎝<br />
3<br />
13<br />
11<br />
⎞<br />
⎟<br />
⎠<br />
⎛ 3 ⎞<br />
= ⎜ ⎟<br />
⎝ 7 ⎠<br />
−9<br />
⎛<br />
= ⎜<br />
⎝<br />
x<br />
3<br />
13<br />
× (iii)<br />
⎞<br />
⎟<br />
⎠<br />
2x+<br />
1<br />
⎛<br />
⎜ −<br />
⎝<br />
2 ⎞ ⎟<br />
9 ⎠<br />
−3<br />
⎛ 2 ⎞ × ⎜ − ⎟<br />
⎝ 9 ⎠<br />
8. Express as a product of primes <strong>and</strong> write the answers of each of the following in<br />
exponential form:<br />
(i) 6480000 (ii) 172872 (iii) 11863800<br />
9. The star sirus is about 8.1 × 10 13 km from the earth. Assuming that the light travels at<br />
3.0 × 10 5 km per second, find how long light from sirus takes to reach earth.<br />
10. State which of the following are surds:<br />
5<br />
36<br />
(i) (ii)<br />
+<br />
289<br />
11. Express as a pure surd:<br />
(i) 3<br />
9 3<br />
4<br />
729 (iii) 5 1 (iv) 3125<br />
2 3<br />
5<br />
3<br />
(ii) 5 4 (iii) 5 2<br />
1<strong>2.</strong> Express as a mixed surd in simplest form:<br />
(i) 4 405 (ii) 5 320 (iii) 3 128<br />
13. Which of the following are pairs of similar surds?<br />
(i) 112 , 343 (ii) 3 3<br />
625 , 3125× 25 (iii)<br />
6<br />
216, 250<br />
70<br />
Mathematics Secondary Course
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