Example 6. Required the 4th power of b+2. b+21st power. 6+2 ba+26 +26+4 ba+4b+4=2d power of b+2. 6+2 b3+4b2+4b +262 +86+8 b3+6b2+126+8=3d power of b+2. b+2 b+663+1262 +86 +263 +1262 +246+16 ba+8b3+24b2+32b+16=the 4th power of b+2. Example 7 Required, the 5th power of +1. x+1=1st power. x+1 x4+4x3+6x+4x+1=4th power of +1. +1 x5+4x+6x3+4x2+x +x+4x3+6x2+4x+1 x5+5x2+10x3+10x2+5x+1=5th power of +1. Example 8. Required the 6th power of 1-b. 1-b-the 1st power. 1-b 1-4b+662-4b3b4=4th power of 1-b. 1-b 1-4b+662-4b3+64 -b÷4b26b3+4b4-b5 1−5b+10b2 −1063+564 —b5—5th power of 1-d. 1-b 1-5b+1062-1063 +5b4 —b5 -b5b10b3+1064-5b5+be 1-6b+15b2-20b3+15b4—6b5+b=6th power of 1—b. 8x4y+6x3y-2x2 -4x3y -3x3y+x 8x+y+2x3y-2x2 -3x2y+x=the answer. Multiply x3+x-5 into 2x2+x+1. x3+x-5 2x2+x+1 Example 2. Reduce √a2x. ART. 271. Vax can be resolved into two factors, a2 and √ Example 3. Reduce 18. √18=√9X √2=√9× √2√3/2=the answer. Example 7. Reduce (a3 —a2b)1⁄2. (a3 — a3b) 1⁄2 = √a3× √a—b⇒a√a—b or a(a—b)s. Example 8. Reduce (54ab). (54a©b)}=(27a)3×(26)}=3a2(2b)}. Example 9. Reduce √98a2x. √98a2x=√49a2 × √2x=7a√2x. Example 10. Reduce a3+a3b3. Va3a3b2 may be resolved into two factors, 3/1+b and 3/a3. And the factor /a3, being the cube root of the cube of a, is a, which prefixed to the other factor =a3/1+b2. ADDITION AND SUBTRACTION OF RADICAL QUANTITIES. Art. 275 .Example 4. Add (36a2y) to (25y)§. By Art. 271. (36a2y)=√36a2 × √y=6a√y (25y)=√25X√y=5y=(6a+5) Example 5. Add 18a to 3√2a. ✓18a= √9X √2a=3√2a. 3√2a+3√2a=6√2a=the answer. Subtraction. From 37b4y, subtract 3/by4. 3/b4y=3/b3×3/by=b3/by √by= /by y3=y×3/by}=(b—y)×3⁄4/by=Ans. From V, subtract 5/x. Vx-x, or x-t, or x-t MULTIPLICATION OF RADICAL QUANTITIES. Example 1. Multiply a into /b. The indices and, reduced to a common denominator, are and . Therefore vax¥b= √/a3b3. Example 2. Multiply 55 into 38. 55X3/8 15/40-15/10X √4=1510x2= 30/10. Example 3. Multiply 2/3 into 33/4. 2√3×33⁄4/4=2(33)† × 3(42 )† = 6 &/432. Example 4. Multiply d into 3/ab. √d × 3⁄4/ab = 3⁄4√/a2b2d3; or, (d3)}×(a2b2) } =3⁄4/a2b3d3. Example 5. Multiply/2ab into 3c 9ad 26. 3a2d C • Example 6. Multiply a(a-x) into (c-d)× (ax)* a(a-x)× (c-d)× (ax)=a√a-xx (c–d)× √ax= (ac—ad) × (a2x—ax2)3. DIVISION OF RADICAL QUANTITIES. Example 2. Divide 103/108 by 53/4. 10/10853/4=23/27=2×3=6. Example 3. Divide 10√27 by 2√3. 10/27-23=5√9=5x3=15. |