Test: Number System- Assertion & Reason Type Questions - Class 8

√4 = ±2, which is not an irrational number.

Correct option is (c) Assertion (A) is true but reason (R) is false.

Explanation:
The statement in the assertion is correct. The sum of two irrational numbers is always an irrational number. This can be proved by contradiction.

Let's assume that the sum of two irrational numbers is a rational number. In that case, we can express the sum as a fraction p/q, where p and q are integers and q is not equal to zero. Since the sum is irrational, at least one of the two numbers being added must also be irrational. Let's say one of them is irrational number a.

Now, we can rewrite the sum as a + (p/q - a). The expression p/q - a is rational because it is obtained by subtracting an irrational number from a rational number.

So, the sum a + (p/q - a) is now irrational + rational, which should be rational according to the reason given in the statement. However, we already assumed that the sum is irrational. This is a contradiction, which means that our assumption was wrong. Therefore, the sum of two irrational numbers is always irrational.

Hence, the reason provided in the statement is the correct explanation of the assertion.

So, Reason is correct.

Now, 7⁸ ፥ 7⁴ = 7^{8 – 4} = 7⁴ (∵ a^p ፥ a^q = a^{p – q}) So, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A)

Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

Since, √5 cannot be written in the form of p/q, therefore it is an irrational number. Hence assertion is correct follows from reason.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Now, (3 + 2√5) x (3 – 2√5) = 3² – (2√5)²

= 9 – 20 = – 11

So, both Assertion and Reason are correct and Reason explains Assertion.

Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

So, Reason is not correct.

One of the rational number lying between two rational numbers x and y is ½ (x + y).

So, Assertion is correct

Correct option is (c) Assertion (A) is true but reason (R) is false.

So, Assertion is correct.

Now, 2 + √3 and 4 – √3 are two irrational numbers Sum = 2 + √3 + 4 – √3 = 6 which is a rational number.

So, Reason is not correct.

Correct option is (c) Assertion (A) is true but reason (R) is false.

So, Reason is true.

Now, 11³ x 11⁴ = 11³⁺⁴ = 11⁷

Here assertion is incorrect but reason is correct.

Correct option is (d) Assertion (A) is false but reason (R) is true.

So, Reason is not correct.

Now,

So, Assertion is correct

Correct option is (c) Assertion (A) is true but reason (R) is false.

So, Reason is correct.

Also, we know that a decimal that ends after a finite number of digits is called a terminating decimal.

Hence Assertion is correct but reason is not the correct explanation of Assertion Correct option is (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).