Question

The smallest natural number by which 300 should be multiplied so that square root of the product is a rational number is
a)3
b)5
c)7
d)11​

Answer 1

Answer:

3 is ur answer hope it helps u

Answer 2

The smallest natural number by which 300 should be multiplied so that square root of the product is a rational number is option a) 3

Step-by-step explanation:

A number has its square root rational, if and only if it is a perfect square.

We will multilpy 300 by each given option and check if the square root is rational.

For Option, a) 3

We have,

$(300)(3)=900$

and$\sqrt{900}=30$

As 30 is a rational number option a) is correct.

For Option, b) 5

We have,

$(300)(5)=1500$

and$\sqrt{1500}=10\sqrt{15}$

As $10\sqrt{15}$ is not a rational number option b) is incorrect.

For Option, c) 7

We have,

$(300)(7)=2100$

and$\sqrt{2100}=10\sqrt{21}$

As $10\sqrt{21}$ is not a rational number option c) is incorrect.

For Option, d) 11

We have,

$(300)(11)=3300$

and$\sqrt{3300}=10\sqrt{33}$

As $10\sqrt{33}$ is not a rational number option d) is incorrect.