###### Advertisements

###### Advertisements

Find a rational number between `sqrt(2) "and" sqrt(7)`.

###### Advertisements

#### Solution

We know

`sqrt(2) = 1.414`

`sqrt(7) = 1.732`

So, rational number between `sqrt(2) "and" sqrt(7)` will be 1.5 = `3/2`.

#### RELATED QUESTIONS

Classify the numbers 5.636363 as rational or irrational :

Express 0.`bar(4)` as a rational number simplest form.

Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

What can you say about the prime factorisations of the denominators of the following rationals: \[27 . \bar{{142857}}\]

What can you say about the prime factorisations of the denominators of the following rationals: 0.120120012000120000 ...

State whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

`15/1600`

Write down the decimal expansion of the following number which have terminating decimal expansion.

`29/343`

Find a rational number between `sqrt(2) " and sqrt(3) `.

Find after how many places of decimal the decimal form of the number `27/(2^3. 5^4. 3^2)` will terminate.

The following real number have decimal expansions as given below. In the following case, decide whether it is rational or not. If it is rational, and of the form p/q what can you say about the prime factors of q?

0.120120012000120000. . .