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

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

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

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)

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

π/4 is a ___________

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

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