Square root of 4
Square root is described with the symbol √. If n is an integer than square of n is equal to m which is also an integer. If n2 = m, then n=√m. The square root of 4 is written as √4. Let us explore the square root of 4 in detail.
- Square Root of 4: √4 = 2
- Square of 4: 42 = 16
|1.||What Is the Square Root of 4?|
|2.||Is Square Root of 4 Rational or Irrational?|
|3.||How to Find the Square Root of 4?|
|4.||FAQs on Square Root of 4|
What Is the Square Root of 4?
Let us first understand the meaning of square root. The square root of a number is the number which, when multiplied to itself, gives the product as the original number.
Consider the example:
- 22 = 2 × 2 is 4
Here 2 is called the square root of 4. 4 is a perfect square. So the square root of 4 is 2. Non-square numbers also have a square root, just that they are not whole numbers.
For real numbers a and b,
- a2 = b
- This means that a is the 2nd root of b.
The square root of 4 in the radical form is expressed as √4 and in exponent form, it is expressed as 4½
The square root of 4 is the inverse operation of squaring 2 and -2
- 2 × 2 = 4
- (-2) × (-2) = 4
Is the Square Root of 4 Rational or Irrational?
How to Find the Square Root of 4?
Let us find the square root of 4 using prime factorization:
- 4 = 2 × 2
- √4 = √22
- √4 = (22)½
- By the law of exponents, considering the powers alone, 2 × ½ = 1.
- (22)½ = 2
- √4 = 2
Let us now try finding the square root of 4 by the long division method!
Square Root of 4 By Long Division
Let us follow the steps to find the square root of 4 by long division.
- Step 1: Group the digits into pairs (for digits to the left of the decimal point, pair them from right to left) by placing a bar over it. Since our number is 4, let us represent it as inside the division symbol.
- Step 2: Find the largest number such that when you multiply it with itself, the product is less than or equal to 4. We know that 2 × 2 is 4 and is equal to 4. Now let us divide 4 by 2
Thus the complete process of the long division stops here as the remainder is 0. Thus, the quotient 2 is the square root of 4.
Explore Square roots using illustrations and interactive examples
- Evaluate the following:
3√2 + 7√2 + 10√2
4√4 + 5√4 - 10√25
- The square root of 4 in the radical form is expressed as √4.
- In exponent form, the square root of 4 is expressed as 4½
- The real roots of x2 - 4 = 0 are ±2.
Square Root of 4 Solved Examples
Help Alex find the square root of 4 using the prime factorization method.
√4 = √(2 × 2)
√4 = √22
√4 = 2
The square root of 4 is 2.
Can you help Jane solve the following problem? Find the square root of 4 by repeated subtraction method.
In the repeated subtraction method, we subtract the odd numbers starting from 1 until we get a 0. The number of iterations till we get a 0 is the square root of the number.
4 - 1 = 3
3 - 3 = 0
Since the number of iterations is 2, therefore the square root of 4 is 2.
FAQs on Square Root of 4
What is the square root of 4?
As we learned on this page, the square root of 4 can be either 2 or -2.
What is the square of 4?
The square of 4 is 16. 42 = 16
What is the square of minus 4?
The square of minus 4 is 16.
Is the square root of 4 a rational number?
The square root of 4 is 2, which is a rational number.
Therefore, the square root of 4 is a rational number.
What is the square root of 4 in the simplest radical form?
√4 is the simplest radical form.