ACT Math - How to find the square of an integer

When you square the following numbers, which one results in an irrational number?

$\sqrt2$

$\pi$

$\frac{1}{3}$

$\frac{7}{17}$

$\frac{1}{2}$

Explanation

A rational number is any number than can be expressed as a fraction or a quotient of two integers. The square of π is still an irrational number. (√(2))2 = 2, (1/3)2 = 1/9, (7/17)2 = 49/289, (1/2)2 = 1/4, all can be writen in fractional form, and are thus, rational numbers.

Solve: 3³

Explanation

When using a cube root. 3³ becomes 3 * 3 * 3.

3 * 3 = 9

9 * 3 = 27

If (x - 3)2 = 64, what is a possible value of x?

-5

-8

Explanation

In order to solve for x, we must first take the square root of both sides.

(x - 3)2 = 64

(x - 3) = +/- 8

The square root of 64 is either 8 or -8. We then solve the equation with both possible values of the square root of 64.

x - 3 = 8 (Add 3 to both sides.)

x = 11

x - 3 = -8 (Add 3 to both sides.)

x = -5

x = 11 or -5. -5 is the only possible value of x that is an answer choice.

The last two digits in the square of a number have a product of . Which of the following could NOT be the last digit of ?

Explanation

If the last two digits of the squared number multiply to , then the digits must be factors of . The last digit of any square of a number ending in will be , which is not a factor of . Thus, the number cannot end in .