Question

Which irrational number can be multiplied by -47 to get a product that equals 1?

a) √2
b) -1/√47
c) -√47
d) 1/√47

Answer 1

The irrational number that can be multiplied by -47 to get a product of 1 is option b) -1/√47, which is the multiplicative inverse of -47.

Step-by-step explanation:

To find the irrational number that can be multiplied by -47 to get a product of 1, we need to find the multiplicative inverse of -47, which when multiplied by -47 will give us 1.

Looking at the options provided:
a) √2 is not related to 47, so it is not the inverse of -47.
b) -1/√47 when multiplied by -47 gives us 1 because the negative signs cancel out and 47/√47 equals √47, which when multiplied by 1/√47 gives 1.
c) -√47 if multiplied by -47 would give a positive number, but not 1.
d) 1/√47 would give a positive fraction when multiplied by 47, not 1.

Therefore, the correct answer is option b) -1/√47.

Answer 2

The correct answer is b) -1/√47.

Step-by-step explanation:

To find the irrational number that, when multiplied by -47, yields a product of 1, we can set up the equation:

x * (-47) = 1

Solving for x, we divide both sides by -47:

x = 1/(-47)

Now, to express this fraction with a rationalized denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √47:

x = (1 * √47) / (-47 * √47)

Simplifying further:

x = √47 / (-47 * √47)

This can be simplified to:

x = -1/√47

So, the irrational number that, when multiplied by -47, equals 1 is -1/√47, corresponding to option b.

In summary, by setting up the equation and solving for x, we determine that the correct answer is -1/√47, which can be rationalized to -1/√47. Therefore, option b) is the correct choice.