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
I assume you want to simplify
5/7 √(3/2)
= 5/7 √(6/4)
= 5/7 * 1/2 √6
= 5/14 √6
I can't read it.
To simplify the expression 5/7�ã3/2, we need to rationalize the denominator.
Step 1: Start by writing the expression as a fraction: (5/7) * (�ã3/2).
Step 2: Rationalize the denominator by multiplying the numerator and denominator of the square root expression by the conjugate of the denominator, which is �ã2: (5/7) * (�ã3/2) * (�ã2/�ã2).
Step 3: Simplify the expression by multiplying the numerators and denominators together: (5 * �ã3 * �ã2) / (7 * 2).
Step 4: Multiply the square roots together under one radical sign: (5 * �ã6) / 14.
Therefore, the simplified expression is (5�ã6) / 14, and the value of b is 14.
Therefore, the correct answer is D) 14.
To solve this question, we need to simplify the given fraction, 5/7�ã3/2.
First, let's simplify 3/2. The square root of 3/2 can be found by separately taking the square root of the numerator (3) and the denominator (2).
√(3/2) = √3 / √2
Now, the fraction becomes 5/7 * (√3 / √2).
To simplify further, we multiply the numerators and denominators:
5 * √3 / 7 * √2
This gives us (√15 / 7√2).
To represent this fraction as a�ãb, where a is a real number and b is an integer, we need to rationalize the denominator.
Rationalizing the denominator means multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of 7√2 is -7√2.
So, multiplying (√15 / 7√2) by (-7√2 / -7√2) gives us:
(-7√30) / (-14)
Finally, we can rewrite the fraction as a�ãb, where a is a real number and b is an integer.
The fraction -7√30 / -14 can be simplified to a = √30 and b = 2.
Therefore, the value of b is 2.