Tab 1
, Class - 10
____________REAL NUMBER________
Question - 1 // Prove that ✓2 is an irrational number …………..( always coming in board
paper)
Answer // let √2 is rational number and co-prime number
√2 =p/q
Square both sides
(√2)² = p²/q²
2q² = p²
q² = p² ÷ 2
Or
q² = p²/2
Here p² is divisible by 2
So, p is also divisible by 2 ……(1st)
Let ,
p=2
By first
q² = (2p)² ÷ 2
q²= 4p²/2
q² = 2p²
q²÷ 2 = p²
Or
q²/2 = p²
Here p² is divisible by 2
So, p is also divisible by 2
Here,
2 is common factor of p and q but p and q are co-prime number
So,
Our Assumption is wrong
Hence,
√2 is an irrational number
, Class - 10
____________REAL NUMBER________
Question - 1 // Prove that ✓2 is an irrational number …………..( always coming in board
paper)
Answer // let √2 is rational number and co-prime number
√2 =p/q
Square both sides
(√2)² = p²/q²
2q² = p²
q² = p² ÷ 2
Or
q² = p²/2
Here p² is divisible by 2
So, p is also divisible by 2 ……(1st)
Let ,
p=2
By first
q² = (2p)² ÷ 2
q²= 4p²/2
q² = 2p²
q²÷ 2 = p²
Or
q²/2 = p²
Here p² is divisible by 2
So, p is also divisible by 2
Here,
2 is common factor of p and q but p and q are co-prime number
So,
Our Assumption is wrong
Hence,
√2 is an irrational number
