Operations on Real Numbers | Number Systems | Assessment | English | Grade 9

The sum or difference of a rational number and an irrational number is a _______.

• Irrational Number

• Whole number

• Rational Number

• Natural Number

Answer explanation

The sum or difference of a rational number and an irrational number is an irrational number. For example: 5 +√20 5 is a rational number and √20 is an irrational number √20 = 4.472135.......Non - terminating non - recurring 5+√20 is also an irrational number 5+√20= 5 + 4.472135...= 9.472135...

Multiply : 4√5 by 2√5

• 8√5

• 40

• 5√8

• 60

Answer explanation

4√5 x 2√5 = 4 x 2 x √5 x √5 = 8 x 5 = 40

Add : 2√3 + 5√2 and √3 - 3√2

• 3√3 + 2√2

• 2√3 - 3√2

• 3√3 - 2√2

• 2√3 + 3√2

Answer explanation

2√3 + 5√2 and √3 - 3√2 = 2√3 + 5√2 + √3 - 3√2 = (2√3 + √3)+ (5√2 - 3√2) = 3√3 + 2√2

Simplify the following Expression : (7 + √6) (7 - √6)

• 49√6

• 13

• 43

• 36√7

Answer explanation

(7 + √6) (7 - √6) = 7² - (√6)² = 49 - 6 = 43

π/4 is a ___________

• Rational Number

• Irrational Number

• Fraction

• Whole number

Answer explanation

π/4 = 3.141592...../4 = 0.7853.... Now here, the decimal expansion of this number is non terminating and non recurring and such numbers are known as Irrational Numbers. Hence, π/4 is an irrational number. Also, when we divide an irrational number with a rational number, the answer will be irrational only.

Simplify the following Expression : (√5 + √7)²

• 6 + 2√35

• 12√35

• 12 + 2√35

• 5√35

Answer explanation

(√5 + √7)² By using Identity - (√a + √b)² = (√5)² + 2√5 x √7 + (√7)² = 5 + 2√35 + 7 = 12 + 2√35

Which of the following is a rational number?

• (3 + √2)²

• (2 - √2)²

• (√5 - √3)²

• [2/(3√2)]²

Answer explanation

In Option 1, (3 + √2)² = (3)² + 2(3)(√2) + (√2)² = 9 + 6√2 + 2 = 11 + 6√2 ....(Irrational number) In Option2, (2 - √2)² = (2)² - 2(2)(√2) + (√2)² = 4 - 4√2 + 2 = 6 - 4√2 ....(Irrational number) In Option 3, (√5 - √3)² = (√5)² - 2(√5)(√3) + (√3)² = 5 - 2√15 + 3 = 8 - 2√15 ....(Irrational number) In Option 4, [2/(3√2)]² = (2)²/(3√2)² = 4/18 = 2/9 ....(Rational number) Therefore, option 4 is the correct answer