Question

Please answer Find a rational number between -3/7 and 1/3 please write the steps...and the rational number between ✓3 and ✓5 .. simplify :(✓3-✓5)²

Answer 1

There are infinite numbers of rational numbers in between (-7/3) & (1/3).as well as in between the √3 & √5.
now (√3-√5)
=(√3)^2 -2(√3)(√5)+(√5)^2
=3+5-2(√15)
=8-2(√15)

Answer 2

We have to find a rational number between. (-3/7) and (1/3)

The first step is to make the denominators same

So, taking the lcm and solving the first two given fractions.

So,

(-3/7) and (1/3)

We will multiply 3 in first fraction and 7 in second fraction .
So,
The fractions become

(-3*3/7*3) and. (1*7/3*7)
Or,

(-9/21). And (7/21)


Between these two numbers we can easily find a fraction or rational number.

Before that
A rational number is a number which can be expressed in the form p/q where p and q are integers and co-primes and q is not equal to 0.

So,

Such a number between (-9/21) and (7/21) can be
3/21 = 1/7
Or, (-7/21). = (-1/3)


A rational number between root 3 and root 5

First we will convert both these into decimals
So,
Root 3 is equal to 1.732
And, 2.236 is equal to root 5 (approximately)

Now,
A rational number can be a decimal but it must be terminating or non terminating but repeating decimal.

So, such a decimal between root 3 and root 5 can be
2.00
Or, 2.12121212.......


Simplification of (root 3 - root 5)^2

So,
Using the formula of (a-b)^2 = (a)^2 + (b)^2 -2ab

Applying this the sum becomes

(Root 3)^2 + (root 5)^2 - 2 root 3 root 5

3+5 - 2root15

Or, 8 - 2 root 15.