Question

Consider the numbers 4 and 5√. Which operation(s) will result in an irrational number?

Answer 1

Answer:

it's 5√

Step-by-step explanation:

because it has square root

Answer 2

COMPLETE QUESTION

Consider the numbers 4 and √5 Which operation(s) will result in an irrational number?

A. the sum only

B. the product only

C. neither the sum nor the product

D. both the sum and product

ANSWER

The correct answer is option (D) Both the sum and product.

Given

Numbers 4 and √5

TO FIND

Which among the following operations will result in an irrational number.

SOLUTION

We can simply solve the above problem as follows

We know that,

4 is a rational number as it can be expressed in form of fractions and it is a terminating and non-recurring number.

√5 is an irrational number as it cannot be represented in the form of a fraction and is a non-terminating and recurring number.

A. Sum of 4 and √5

4 + √ 5 = 4 + √5

as the value of √5 = 2.236967.........

if we add 4 to this number we get,

4 + 2.236967... = 6.2.236967.....

Which is also non-terminating and non-recurring.

Hence, the sum of 4+√5 is irrational.

B. Product of 4 and √5

4 × √5 = 4√5

As the value of √5 = 2.236967.........

If we multiply 4 by this number we get,

4× 2.236967... = 8.2.236967....

Which is also non-terminating and non-recurring.

Hence, the product of 4 and √5 is irrational.

So, the correct answer is (D) both the sum and product

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