Question

Can someone help me with number 23?

Answer 1

Answer:

See explanation

Step-by-step explanation:

It is impossible to take the square root of a negative number. Try any value, nothing works. $2^2 = 4$, and $-2^2 = 4$. It just doesn't work. This is why there is no real number that satisfies $\sqrt{-4}$ (however it is represented as $2i$, i being "the imaginary number" that mathematicians made up to represent it).

When we are finding the cube root of a number, we are looking for a number that when multiplied by itself 3 times, will equal the number.

This is different than squared. Any number, positive or negative, squared will be positive. However, we can test out values and see we can end up with a negative when cubing.

For example: $5^3 = 5\cdot 5\cdot 5 = 125$

HOWEVER:

$-5^3 = -5 \cdot -5 \cdot -5 = -125$

We know that $2^3 = 8$, this means that $-2^3 = -8$ (as $-2 \cdot -2 \cdot -2 = -8$)

Hope this helped!