C It is a square root of a non-perfect square
A rational number is one that can be expressed as the ratio of two integers. The given decimal is a repeating decimal, which means it can be expressed as a fraction.
To show that it is a square root of a non-perfect square, we first need to realize that the decimal 0.747447444744447444447... can be written as 7/10 + 4/100 + 74/1000 + 744/10000 + 7(4444...)/10000000... = 7/10 + 4/100 + 74/1000 + 744/10000 + 7/(10^n) * (4444...)/(10000...), where n represents the number of 4's after the decimal point.
Now, let's simplify this expression as a fraction. We can rewrite it as (7/10 + 4/100 + 74/1000 + 744/10000)/(1 - 1/10^n).
The numerator is a finite sum of fractions, which is a rational number. The denominator, 1 - 1/10^n, is also a rational number because it is the difference of two rational numbers. Therefore, the entire expression is a rational number.
Hence, the given decimal is a rational number.
PLEASE HELP ME
pick one of the answers below to explain why 0, point, 7, 4, 7, 4, 4, 7, 4, 4, 4, 7, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 7, point, point, .0.747447444744447444447... . is a rational number:
A It is a decimal that does terminate
B it is the square root of a perfect square
C it is a square root of a non-perfect square
1 answer
1 answer