I don't know how to solve this...
Question: Suppose 5/7�ã3/2 is written in simplest form as a�ãb, where a is a real number and b is an integer. What is the value of b?
(The square root is over the whole fraction of 3/2)
A 2 B 3 C 6 D 14
I think it is either A or B
Ok, I can't read your symbols.
is it
(5/7)√(3/2) ?
or
5/(7√(3/2) )?
Been there, done that:
http://www.jiskha.com/display.cgi?id=1468110223
b=6
To solve this question, you need to simplify the given fraction, 5/7�ã3/2, to its simplest form. The square root over the whole fraction of 3/2 is indicated by the symbol �ã.
To simplify the fraction, you need to rationalize the denominator, which means eliminating the square root from the bottom part of the fraction.
To do this, multiply both the numerator and the denominator by the conjugate of the denominator, which is the same as the denominator but with the opposite sign of the square root. In this case, the conjugate of √(3/2) is -√(3/2).
So, your fraction becomes:
(5/7)�ã3/2 * (-�ã3/2) / (-�ã3/2)
Simplifying the numerator:
5 * -�ã3/2 * -�ã3/2 = -15/4
Simplifying the denominator:
(-�ã3/2) * (-�ã3/2) = -3/2
Now, you have:
-15/4 / -3/2
To divide fractions, multiply the first fraction by the reciprocal of the second fraction:
-15/4 * 2/-3
Simplifying further:
= (-15 * 2) / (4 * -3)
= -30 / -12
= 5/2
So, the simplified form of the given fraction is 5/2.
Now, looking at the answer choices, we need to find the value of b, which represents the integer part of the simplified fraction. In this case, b is equal to 2.
Therefore, the correct answer is B: 3.