Question

how, to show underfoot 4 as a rational number​

Answer 1

A number is rational if and only if it can be expressed as a fraction where the numerator and denominator are both integers. For example, .3333333… is rational because it can be expressed by the fraction 1/3. Note that any integer can simply be expressed as itself/1; therefore, all integers are rational number.

The most commonly used irrational numbers are roots, such as √2. However, not all roots are irrational. Integers that are perfect squares can have their square root cleanly taken. √4 = 2 because 2^2 = 4. 2 is an integer and thus a rational number. Thus, we conclude that √4, being the same as 2, is also rational.

Answer 2

Question:-

Prove that √4 is a rational number

${\blue{\underline{\underline{\bold{Solution:-}}}}}$

√4 is rational number and can be written as $\frac{m}{n}$ where n≠0

$\frac{m}{n}$ is in lowest reduced terms; i.e. m and n are co-prime due to definition of rational numbers

Then I took the following steps:

${m}^{2}=4{n}^{2}$

${m}^{2}=2(2{n}^{2})$

Thus,${m}^{2}$is even ⟹ m is even and can be written as 2k.

${m}^{2} =4{k}^{2}=4{n}^{2}$

k=n

Thus, k is a factor of both m and n, contradicting the second assumption that I made (m and n are co-prime).

Thus √4 is a rational