Math thinking question?

Question

How would you explain square roots, cube roots, nth roots, and radicals . What are some limitations of square root

Answer 1

The square root of a number is the number which, when squared (multiplied by itself) gives you the original number. Similarly, the cube root is the number which when cubed (raised to the third power) gives you back the original number. For example, the square root of 9 is 3 (because 3 squared, or 3x3, is 9). The cube root of 64 is 4 (because 4 cubed, or 4x4x4, is 64). "nth" roots describe the same general idea, just extended to powers of n. For example, the 5th root of 32 is 2, because 2 to the 5th power (2x2x2x2x2) is 32.

A "radical" is just the symbol that means taking the root of a number. It looks like a checkmark. This means the square root, but if there's a number before it, it means that root number. For example, √9 is the "square root of 9" whereas the cube root of 27 would be written as something like ³√27.

Some of the limitations to square roots are: 1) it's not always easy to see what the square root of a number will be. When you take the square root of a number like 10, you're going to have a long decimal number that's somewhere in between 3 and 4. Also, 2) You can't take the square root of a negative number. Since two negative numbers multipled together produce a positive number, as does two positive numbers multiplied together, there's no number that when multiplied by itself produces a negative number. In higher levels of math, you find "imaginary numbers", where you can pretend to take the square root of negative numbers in a special way and do useful things with the results, but generally speaking, taking the square root of a number is off-limits.

Answer 2

To explain roots in general is best done by doing it backwards--like the square root of 16 is either +4 or -4; square root is the number when multiplied by itself ONCE will give the original number. The square root -4 when multiplied again (-4)(-4) will give original number +16.

Similarly, the cube root is the number multiplied three times. For example cube roots of 8 is 2. You get the idea for 4th root and so on.

Radicals mean there is a radical sign and yes the exponents can be fractions. For instance, the expression x^(2/3) means take the cube root of x^2 or x squared. Thus, in radical form, you write this with (x^2) under the radical sign and the number 3 as index (the number between the V part ) of the radical.

The limitatons of the square root is shown usually in the calculation of the sides of a square. Let us say that the area of the square is 25 and you are asked to find the dimensions of the square. This means, find the value of the sides of the square.
Area = 25 = x^2, will give you values of x as +5 and -5.

BUT a side cannot be negative. You cannot measure a side with negative value; it does not have physical significance. So, taking the square root does not necessarily give you the correct answer. You still have to analyze it.

Answer 3

Example: Square root of 49=7 because 7^2=7*7=49.
Square Root of a number x is another number whose square is x.
x must not be negative in this case.
Example: Cube Root of 64 = 4 because 4^3=4*4*4=64.
Cube Root of a number x is another number whose cube is x.
There is no limitation on x.
and so on.

nth Root of a number x is a number whose nth power is x.
For square root, n=2; for cube root, n=3 etc.
Square Root of a number which is not a square of a rational number is called a radical. Similarly,Cube Root of a number which is not a cube of a rational number is called a radical and so on.

Answer 4

A number raised to a power consist of two parts. An exponent and a Base, the exponent only tells you how many times the base is used as a factor in a multiplication problem.
A square root, for example, is taking a number and extracting the base, or the root number.
Example five is the square root of 25 because five is the base raised to the second power to equal 25.
in other words, one process is the opposite of the other. One takes the base and uses it as a factor to arrive at the new number. The other takes the new number and extracts the base that was used to arrive at the new number.

Answer 5

square root is wat number time it self would = x number. the nuber u are squaring can't be negative. cube root. same 3 num's that would = x number. Can't be fractions. redicals are fractions it can't be x/0 u can divide by 0.