Introduction
The square root of 12 in mathematical form is written with a radical sign like this\[ \sqrt{12} \] . The square root of 12 in radical form is called the square root. Square root is denoted by the sign "\[ \sqrt{} \] "also known as the radical symbol or radix. The radicand is the number that appears behind the radical symbol or radix.
The Value of the Square Root of 12
The root of 12 is denoted by the symbol \[ \sqrt{12} \]. The number 12 is not a prime number, but it is an even number. Prime numbers, such as 1, 3, 5, contain only two factors: 1 and the number itself. As we know, 12 have six factors, 1, 2, 3, 4, 6, and 12 itself, such as,
1 × 12 = 12
2 × 6 = 12
3 × 4 = 12
4 × 3 = 12
6 × 2 = 12
12 × 1 = 12
How can we find the square root of 12?
12 = 2 × 2 × 3
In the preceding phrase, only one square number is available on the right.
Taking the square term out of the root we get,
\[ \sqrt{12} \] = 2 \[ \sqrt{3} \]
This is the radical form of \[ \sqrt{12} \] . In decimal form, the value is \[ \sqrt{3}\], or 1.73.
\[ \sqrt{12} \] = 2 × 1.73
\[ \sqrt{12} \] = ± 3.46 approximately.
What is the Square Root of 12 in Exponent Form?
The square root of 12 is expressed as \[ \sqrt{12} \] in the radical form and as (12)½ or (12) 0.5 in the exponent form. The positive answer to the equation x2 = 12 is 3.46410, which is the square root of 12. The radical version of the 12 square root is 2 \[ \sqrt{3} \].
Square Root of 12: 3.4641016151377544
Square Root of 12 in exponential form: (12)½ or (12)0.5
Square Root of 12 in radical form: √12 or 2 \[ \sqrt{3} \]
Is the Square Root of 12 Rational or Irrational?
Suppose you can't write a number down as the sum of two integers. This means that the decimal form of the irrational number will not end or repeat itself (i.e., the decimal part of the number never repeats a pattern).
\[ \sqrt{12} \] = 3.4641016151
How to Solve Exponential Powers?
All square roots could be changed into a number with a fractional exponent, and this can be done for all of them. The square root of 12 isn't different. The square root of 12 transformed to a base with an exponent?
\[ \sqrt{b} \] = b½
\[ \sqrt{12} \] = 12½
Some Other Square Root
FAQs on Square Root of 12 - Value, Calculating Method, Solved Examples
1.The value of -(\[\sqrt{12}\]) is the same as (\[\sqrt{-12}\]). What are your thoughts?
A negative square root cannot have real roots.
-(\[\sqrt{12}\]) has real roots, but (\[\sqrt{-12}\]) has only imaginary roots.
Hence, they are not the same. (\[\sqrt{-12}\]) is not the same as (-\[\sqrt{12}\]).
2. What is the square root of 12 to its lowest radical form?
We need to express 12 as the product of its prime factors.
12 = 3 × 2 × 2
Therefore, \[ \sqrt{12} \] = \[ \sqrt{{ 3 × 2 × 2}}\] = 2\[\sqrt{3}\]
Thus, 2\[ \sqrt{3}\] is in the lowest radical form.
3. What is the square root of 12 rounded?
Using the square root of 12 and rounding to the closest tenth, you'll need one digit after the decimal point to complete the calculation. Using the square root of 12 and rounding to the closest hundredth, you'll need two digits after the decimal point to represent the answer correctly. Using the square root of 12 and rounding to the nearest thousandth, you must have three digits after the decimal point in your answer.
10th: \[ \sqrt{12} \] ≈ 3.5
100th: \[ \sqrt{12} \] ≈ 3.46
1000th: \[ \sqrt{12} \] ≈ 3.464
4. What is the square root of 12 as a fraction?
Since the square root of 12 is an irrational number, we cannot convert it into a proper fraction. We can, however, approximate the fraction by taking the square root of 12 and rounding it to the nearest hundredth.
\[ \sqrt{12} \]
≈ 3.46/1
≈ 346/100
≈ 323/50
5. What two numbers fall between the square root of 12?
12 lies between 9 and 16, so \[ \sqrt{12} \] lies between 3 and 4.
6. Can there be two square root of a number?
We know that 9 was the square of 3 Thus the square of -3 is also 9. All positive real numbers have two square roots. positive square root and negative square root. The positive square root is commonly referred to as the principal square root. The main reason that a number could have two square roots is that the product of two numbers is positive if both numbers have the same sign.
A square root is a radical symbol √ and the number inside the radical symbol called the radicand.
for both the positive and the negative square root of a radicand we put the symbol ± (read as plus-minus) in front of the root ±9=±3.
7. Is \[\sqrt{2} \] x \[ \sqrt{2}\] equals to 2.
When we Recall the meaning of a square root of a number which is a value when multiplied by itself gives us the desired number
\[ \sqrt{2}\] can also be written as 21/2
So when 21/2 * 21/2
When multiplied with the same base powers will be added here in this ½ + ½ = 1
That means 2 has exponent 1 which gives as 21