Find the value of b if 532b is a perfect square and 7b507 is a perfect cubej
Answers
Answer:
Step-by-step explanation:
It is not tough as it looks !
Step1-
find the nearest perfect square to 532b.
1, 4, 9, 25, 36, 49, 64....
The number 532b must be a perfect square between 4900 (70 square ) and 6400 (80 square ).
Step 2
Trail and error method
71 square = 5041
72 square = 5184
73 square = 5329 ==> this is the no.
74 square = 5476
74 square is higher than our required number .
So the answer is 5329 .
There fore b = 9
There won’t be any need to verify the cube number . 79507 Will be a perfect cube
Concept:
The solution of this problem can be found through hit and trial method because we not have any concrete values given.
Given:
523b: Perfect square
7b507 : Perfect cube
To find:
The value of b,
if 523b is perfect square and 7b507 is a perfect cube.
Solution:
Given that the number 523b is a perfect square.
This number lies between the perfect square numbers 4900 and 6400.
4900, being the perfect square of 70 and 6400 being the perfect square of 80.
On applying the hit and trial method,
The squares for the numbers in between are-
71: 5041
72: 5184
73: 5329.
We have got our answer. On comparing 523b with 5239, b= 9
To check,
79507 is a perfect cube of 43.
Hence, the answer is 9.