Eg: 4^2=4*4 ; in this equation 2 is called power of 4,4 is called base
Power of a number means:multiply of a particular number with itself
till the power of a number.more eg are given below: 13^3=13*13*13 , 23^3=23*23*23;
Square of a number : it means multiply with the no. itself Eg: 45^2 = 45*45
cube of a number:it means multiply the no. with itself 3 times Eg:80^3=80*80*80
square root: Eg:36 =6*6 square root of 36=6 , 64=8*8 square root of 64=8
cube root : Eg: 512=8*8*8, 216=6*6*6 ,so cube root of 512=8 .
(x)-b/a = (1/x)b/a ,(x/y)-b/a= y/xb/a
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1.Find the square of 15
Ans:15*15=225
2.Find the cube of 15
Ans:15*15*15=3375
3.Find (2/3) 5
Ans:(2/3)*(2/3)*(2/3)*(2/3)*(2/3)=64/234
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Prime factorization method to find the square root and cube root of any no:
a)1024 2| 1024
2|512
2|256
2|128
2|64
2|32
2|16
2|8
2|4
2|2
1
2*2,2*2,2*2,2*2,2*2.so square root be 2*2*2*2*2=16 |
b)250000 2|250000
2|125000
2|62500
2|31250
5|15625
5|3125
5|625
5|125
5|25
5|5
1
2*2,2*2,5*5,5*5,5*5.so square root would be 2*2*5*5*5 =500 |
prime factorization method to find the cube root of any no:
a) 4096 2|4096
2|2048
2|1024
2|512
2|256
2|128
2|64
2|32
2|16
2|8
2|4
2|2
1
2*2*2,2*2*2,2*2*2,2*2*2 so the cube root would be 2*2*2*2=16 |
b) 125,000,000
5|125000000
5|25000,000
5|5,000,000
5|1,000,000
5|200,000
5|40,000
2|8,000
2|4,000
2|2,000
2|1,000
2|500
2|250
5|125
5|25
5|1
5*5*5,5*5*5,5*5*5,2*2*2,2*2*2 ,so cube root would be 500. |