Question

Explain why the absolute value of a number is never a negative number.

Answer 1

Answer:

The reason why the absolute value of a number is never a negative number is because absolute value implies the positive value of the number.

To put it in other words, absolute value cannot be negative because it's always positive.

The function of y=|x| (absolute value function) will give the positive value of x. So if x=-1, |x|=1

If x=1, |x|=1

Hope it helps!

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Answer 2

The absolute value of a number is never a negative number.

• Let's consider a number x for the calculation of its absolute value.
• The absolute value of a number is calculated as,

         $(\sqrt{x} )^{2}$

• Let the square root of x be equal to y.

        $\sqrt{x} = y$

• The square root of x can have two values, +y and -y.
• But to find the absolute value of x, the values of y must be squared.

        $(+y)^{2} = +y^{2}$

        $(-y)^{2} = +y^{2}$

• Any number, positive or negative, on squaring can give a positive number only.

        $(\sqrt{x} )^{2} = +y$

• Hence, the absolute value of a number is never a negative number.