Answer: b) 7 and 8
Step-by-step explanation:
The formula for calculating the square root of non perfect square is given as :
square root of non perfect square = square root of the nearest lower perfect square + (difference between the number and the perfect square)/ 2x the perfect square.
To find the square root of 52.
The nearest lower perfect square to 52 is 49 , applying the formula , we have:
[tex]\sqrt{52}[/tex] = [tex]\sqrt{49}[/tex] - [tex]\frac{52-49}{2\sqrt{49}}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{2(7)}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{14}[/tex]
This shows clearly that [tex]\sqrt{52}[/tex] is between the integer 7 and 8
