The number line
-2, -1, 0, 2, 2.645.... , 3, 4, 5. .....
.-2, -1, 0, 2, sqrt(7) , 3, 4, 5. ......
NB The irrational number sqrt(7) = 7^(1/2) = 2.645751311......
Casually, since 'sqrt(7)' is irrational , it means the decimal digits go to infinity, AND there is no regular order in the decimals numbers.
NB The dots after a number ' ....' mean to mathematicians that the number recurs to infinity.
Negative square root is -√Square root of negative one is i.
When dealing with real numbers, you cannot take the square root of a negative number. The concept of the imaginary number was created to handle the square root of a negative number.That's almost like saying "when dealing with numbers bigger than 10, you cannot take the square root of 4. If what you are dealing with does not represent a number, then you cannot find its square root.
The radical symbol ( √ ) followed by a line above what's in the radical, designates positive square root.
Mathematicians decided that, since the square root of a negative number does not exist, they would use the first letter of "imaginary" to represent this "value".
Hope that you have understood how to represent root 5 on the number line. For reference go figure given below the first video in this lesion. Now, draw CB ⊥ AB and CB = 1 unit (as shown in first video). Now, join OC. The length of OC is root 6. At C, DC ⊥ AB. Join OD. Taking O as centre and OD as radius draw an arc that intersects the number line Q .Here, OD = OQ = root 7.Now, Q is the point on the number line that represents the number root 7.
take a no. line
You can't find the square root of -10 because you can't find the square root of any negative number. But we have something to represent the answer, i, i is a imaginary number.
......................... ..------------------.. ..|.....|.....|.....|... ..0.....1...√4...3... ........................
2
It represents a number. The number is the one which, when you multiply it by itself, the product is 'n'.
It is no tpossible to find the square root of an unknown number. You can, however, represent it as x0.5 or √x so that the value of the square root can be evaluated when the value of x is known.
It represents another number that, when multiplied by itself, gives the number you started with. For example, the square root of 2.25 is 1.5 because 1.5*1.5 = 2.25
The 'radical': √
friends,root 10 is according to our pythagores thoream.root 10=square of 3 and square of 1 can be represented on a number line.
To represent the square root of 11.5 on a number line, we first need to approximate the value. The square root of 11.5 is approximately 3.39. On the number line, locate the whole number 3 and then estimate the position of 3.39 between 3 and 4. Mark this point on the number line to represent the square root of 11.5.
By root, I think you mean square root. The square root of 2 is approx. 1.414. The square root of 9 = 3, so this goes exactly at 3 on the number line. Square root 2 will be less than 1/2 way between 1 and 2 on the number line.
it is less than 4 greater than 5