Question

is ✓7 a rational no if it is give resin and solve the answers pls

Answer 1

HEYA FRIEND!!

NO √7 IS NOT A RATIONAL NUMBER BECAUSE ITS VALUE WILL COME INTO POINTS AND THAT WILL NEVER BE REPEATED AND RECURRING.
√7 = 2.6457513111


so, there is no rexurring of numbers .so, ut is irrational.

HOPE IT HELOS U

Answer 2

A Rational Number of the form or a number which can be expressed in the form of p/q, where p and q are integers and q ≠ zero, is called a Rational Number. Example : 2 / 3 , -5 / 7, -10 / -3 are Rational Number.

✓7 a irrational nos.

Sol:

let us assume that √7 be rational.

then it must in the form of p / q  [q ≠ 0] [p and q are co-prime]

√7 = p / q

⇒ √7 x q = p

squaring on both sides

⇒ 7q2= p2  ------> (1)

⇒p2 is divisible by 7

⇒p is divisible by 7

⇒p = 7c  [c is a positive integer] [squaring on both sides ]

⇒p2 = 49 c2 --------- > (2)

subsitute p2 in equ (1) we get

⇒7q2 = 49 c2

⇒q2 = 7c2

⇒ q is divisble by 7

thus q and p have a common factor 7.

there is a contradiction

as our assumsion p & q are co prime but it has a common factor.

so that √7 is an irrational. proved