Download 2 +

3.1415926535897932384626433832795028841971693993751058209749445923078
164062862089986280348253421170679821480865132823066470938446095505822
317253594081284811174502841027019385211055596446229489549303819644288
109756659334461284756482337867831652712019091456485669234603486104543
266482133936072602491412737245870066063155881748815209209628292540917
153643678925903600113305305488204665213841469519415116094330572703657
595919530921861173819326117931051185480744623799627495673518857527248
912279381830119491298336733624406566430860213949463952247371907021798
609437027705392171762931767523846748184676694051320005681271452635608
277857713427577896091736371787214684409012249534301465495853710507922
796892589235420199561121290219608640344181598136297747713099605187072
113499999983729780499510597317328160963185950244594553469083026425223
082533446850352619311881710100031378387528865875332083814206171776691
473035982534904287554687311595628638823537875937519577818577805321712
268066130019278766111959092164201989380952572010654858632788659361533
818279682303019520353018529689957736225994138912497217752834791315155
748572424541506959508295331168617278558890750983817546374649393192550
604009277016711390098488240128583616035637076601047101819429555961989
467678374494482553797747268471040475346462080466842590694912933136770
289891521047521620569660240580381501935112533824300355876402474964732
639141992726042699227967823547816360093417216412199245863150302861829
745557067498385054945885869269956909272107975093029553211653449872027
559602364806654991198818347977535663698074265425278625518184175746728
909777727938000816470600161452491921732172147723501414419735685481613
Rational or Irrational?
Are these numbers rational or irrational?
r2
2r2
3 + 4
Irrational
Numbers
3
3 + √2
2
√1 2(√5)2
√25
Rational
√15
√8 x √2
0.37
√5
0.7123
3√5
 √16
0.37
Rational or Irrational?
Are these numbers rational or irrational?
r2
2r2
3 + 4
Irrational
Numbers
3
3 + √2
2
√1 2(√5)2
√25
Rational
√15
√8 x √2
0.37
√5
0.7123
3√5
 √16 0.37
Rules For Surds
• √a X √b = √(ab)
• √2 X √8 = √(16)
• √a ÷√b = √(a ÷ b)
• √8 ÷√2 = √(4)
x = √2
y = √5
Expression
Substitute
x2
x2 y
bx
by
xy
√2√2
b = 2√5
Evaluate
2
√2√2√5 2√5
2√5√2 2√10
2√5√5 2 x 5
√2√5 √10
Rational?
Rational
Irrational
Irrational
Rational
Irrational
x = √2
Expression
y = √5
Substitute
a = (23)
Evaluate
a2
√8√8
8
√8√8√8 √512
a3
a3x √512√2 √1024
√16
ax
√8√2
x2+y2 2 + 5
7
Rational?
Rational
Irrational
Rational
Rational
Rational
Note
p=3 q=√5 r=2√3 s=√15
Evaluate
___________
___________
pqr
6√15
___________
___________
qr+s
3√15
___________
___________
p2-q2
4
___________
___________
(p-q)2
14-6√15
___________
___________
(p-r)(p+r)
-3
FIND THE HYPOTENUSE
Give the Trig values as surds
45
√2
Hypotenuse
___________
___________
Sin 45
___________
1
√2
___________
Cos 45
___________
1
√2
___________
Tan 45
1
___________
___________
1
(sin 45) + (cos 45)
___________
___________
2
2
FIND THE HYPOTENUSE
And the Height
Give the Trig values as surds
60 60
2 units
___________
___________
√3
Height
___________
Sin 60
___________
Cos 60
√3
___________
2
1
2
___________
√3
___________
___________
Tan 60
1
(sin 60) + (cos 60)
___________
___________
2
2
ax2 + bx + c = 0
x2 + 8x + 1 = 0
-8 ± √(82 - 4x1x1)
x=
2x1
x=
-8 ±√60
2
-8 ± 2√15
=
2
=
-8 ±√4√15
2
x = - 4 + √15
0r - 4 - √15