Question

solve quest 47 , please ​

Answer 1

Step-by-step explanation:

square root of p will p power 1/2

and square root of will be q power 1/2.

as we know that a number then only a rational number when it can be written in the form of p/q

Answer 2

p and q are prime numbers.

let p and q be 3 and 5.

so, the given number= √3 + √5.

If possible let √3 be rational number.

we know that the rational number is always in form of p/q where q is not eqaul to zero.

so, √3 = p

q

squaring both sides

=) 3 = p2

q2

=)p2=3q2

so, clearly

3q2 is divided by 3.

and, p2 is divided by 3. [p2=3q2]

also, p is divided by 3.

let p be 3x.

so, (3x)2 = 3q2

=)9x2 = 3q2

=) 9x2 = q2

3

=) 3x2 = q2

so, clearly

3x2 is divided by 3.

and, q2 is divided by 3. [q2 = 3x2]

also, q is divided by 3.

then, p and q having a common factor is 3.

but, p and q having a common factor is 1.

thus, our supoosion is condradicts.

Hence, √3 is an irrational number .

we know that tha sum of irrational number and with any number always gives a irrational number .

so, √p+√q is an irrational number.

proved