Question

of
Which
the
following
expressions would
be true for an
integer 'X' greater
than 1, whose square
root and cube root
are integers a and b
respectively?
A. x2 = x3
B. (a?)3 = (63)3
C. X is a perfect
square.
D. a is
a perfect
square.
​

Answer 1

Answer:

The expression (a^2)^3 = (b^3)^3 is true

Step-by-step explanation:

Given: Integer ‘x’ greater than 1, whose square root and cube root are integers a and b, respectively.

Solution:

X is positive as it is greater than 1.

Square root of x is a.

Cube root of x is b.

The expressions are as follows:

A. x^2 = x^3 - Cannot be true as a and b are not 1.

B. (a^2)^3 = (b^3)^3

 a^2 = x and b^3 = x

 So (a^2)^3 = (b^3)^3 = x. Hence this expression is true.

C. x is a perfect square.

  - Not necessarily. We just know that a is the square root of a.

D. a is a perfect square.

  - Not necessarily. We just know that a is the square root of a.

So Option B is the answer.

Step-by-step explanation: