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taurus [48]
3 years ago
15

I really stuck on this question can someone help me out? What rational number, when multiplied by an irrational number, has a pr

oduct that is a rational number? a. 1/2 b. 1 c. 1/10 d. 0
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
4 0

Answer:

d. 0

Step-by-step explanation:

Given that:

A rational number is multiplied by a irrational number.

And the result is a rational number.

To find:

Such rational number wil be:

a. \frac{1}2

b. 1

c. \frac{1}{10 }

d. 0

Solution:

Let us consider the given options one by one.

Let the irrational number be = \pi

Checking option a.

Multiply \pi and \frac{1}2.

Result is: \frac{\pi}2 which is again irrational.

So, a. is not correct.

Checking option b.

Multiply \pi and 1.

Result is: \pi which is again irrational.

So, b. is not correct.

Checking option a.

Multiply \pi and \frac{1}{10}.

Result is: \frac{\pi}{10} which is again irrational.

So, c. is not correct.

Checking option d.

Multiply \pi and 0.

Result is: 0 which is rational.

So, d. <em>0 </em>is the correct answer.

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Answer:

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<h2>explanation:</h2>

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Which of the following is equal to the expression (8x)^-2/3 (27x)¯1/3
LiRa [457]

The equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

<h3>How to evaluate the expression?</h3>

The expression is given as:

(8x)^-2/3 * (27x)^-1/3

Evaluate the exponent 8^-2/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * (27x)^-1/3

Evaluate the exponent (27x)^-1/3

(8x)^-2/3 * (27x)^-1/3 = 1/4(x)^-2/3 * 1/3(x)^-1/3

Multiply 1/4 and 1/3

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^-2/3 * (x)^-1/3

Evaluate the exponent

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-2/3 -1/3)

This gives

(8x)^-2/3 * (27x)^-1/3 = 1/12(x)^(-1)

So, we have

(8x)^-2/3 * (27x)^-1/3 = 1/12x

Hence, the equivalent expression of (8x)^-2/3 * (27x)^-1/3 is 1/12x

Read more about equivalent expression at

brainly.com/question/2972832

#SPJ1

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