Question

which of the following is irrational
√4+√9 , √5+√9,√1+√9​

Answer 1

GIVEN:

• √4 + √9
• √5 + √9
• √1 + √9

TO FIND:

• Which of following is irrational ?

SOLUTION:

❶ √4 + √9

$\rm{\hookrightarrow \sqrt{4} + \sqrt{9}}$

$\rm{\hookrightarrow \sqrt{2 \times 2} + \sqrt{3 \times 3}}$

$\rm{\hookrightarrow 2 + 3 }$

$\bf{\hookrightarrow 5 }$

❷ √5 + √9

$\rm{\hookrightarrow \sqrt{5} + \sqrt{3 \times 3}}$

$\bf{\hookrightarrow \sqrt{5} + 3}$

❸ √1 + √9

$\rm{\hookrightarrow \sqrt{1 \times 1} + \sqrt{3 \times 3}}$

$\rm{\hookrightarrow 1 + 3 }$

$\bf{\hookrightarrow 4}$

❝ Hence, √5 + √9 is an irrational number ❞

______________________

Answer 2

1- 2+3
=5

2- (5^1/2) +3
=(5^1/2)+3


3- 1+3
=4