Question

The number 312 lies between the perfect cubes___A.(125 and 330) B.( 216 and 330) C(216 and 343) D(300 and 343). So the cube root of 312 lies between the numbers___A.(5 and 6) B.(6 and 7) C.(7 and 8) D.(8 and 9), which means 312 is___ A.(a rational) B.(an rational) number.

Answer 1

The number 312 lies between the perfect cubes 216 and 343.

So the cube root of 312 lies between the number 6 and 7.

This means that the cube root of 312 is an irrational number because it is not a perfect cube root.

Answer 2

Answer:

6 and 7, irrational

Step-by-step explanation:

When we consider the cubes of natural numbers we find that

$6^3 =216 :\\7^3 =343$

The given number 312 lie between these two cubes.

Hence cube root of 312 has to lie between cube roots of these two numbers.

i.e. cube root of 312 lies between 6 and 7

Since $312=8*39$

cannot be a perfect cube of a rational number

HEnce cube root of 312 is an irrational number