Square root of 72
If you are wondering what the square root of 72 is, it is an irrational number that can be approximated to 8.48528. Similar to the square root of other numbers, the square root of a number (72 in this case) is a value that, when multiplied by itself, results in the original number (72). Mathematically, the square root of 72 can be expressed in either radical or exponent form:
-The radical form of the square root of 72 can be expressed as √72.
-Exponent form of the square root of 72: 72^(1/2) or 72^(0.5)
The √ symbol is commonly known as the radical sign or radix. It is used to indicate that the following number, called the radicand, is the value whose square root we are calculating. The radicand is always positioned under the radical sign or radix.
-The radical form of the square root of 72 can be expressed as √72.
-Exponent form of the square root of 72: 72^(1/2) or 72^(0.5)
The √ symbol is commonly known as the radical sign or radix. It is used to indicate that the following number, called the radicand, is the value whose square root we are calculating. The radicand is always positioned under the radical sign or radix.
Calculator for Square Root of 72
If you want to calculate the square root of a number, including the value of the square root of 72, you can use a square root calculator.
Square Root Calculator
Calculation Guide of Square root of 72
Our discussion will focus on the square root of 72, where we will provide a calculation guide and address commonly asked questions such as whether the square root of 72 is rational or irrational and whether 72 is a perfect square.
Below, you will find all the necessary information regarding the calculations for the square root of 72.
Below, you will find all the necessary information regarding the calculations for the square root of 72.
What is the square root of 72?
By definition, the square root of 72 is the number which, when multiplied by itself, yields the value 72. Since 8.48528 multiplied by itself is approximately equal to 72, we can conclude that the square root of 72 is approximately equal to 8.48528.
Therefore,
ANSWER: Square root of 72 ≈ 8.48528
Therefore,
ANSWER: Square root of 72 ≈ 8.48528
Is 72 a Perfect Square?
A perfect square is a number that can be obtained by squaring or multiplying a whole number, also referred to as an integer. Whole numbers are a set of integers that includes 0, 1, 2, 3, 4, 7, 8, and 9. For instance, the number 81 is a perfect square because it can be written as 9², which is the same as multiplying 9 by itself. It is important to note that 9 is a whole number or an integer. Numbers like -5, 7.025, or 5 ½ are not classified as whole numbers. In our example, the square root of 72 is not a whole number, which means that 72 is not a perfect square.
ANSWER: 72 is not a perfect square.
ANSWER: 72 is not a perfect square.
Is the square root of 72 rational or irrational number?
An irrational number is a numerical value that cannot be represented as the quotient of two integers. Unlike rational numbers, they cannot be written as a finite or repeating decimal.
In our case, the square root of 72 cannot be expressed as a ratio of two whole numbers, which means that it is an irrational number.
ANSWER: The square root of 72 can be classified as an irrational number.
In our case, the square root of 72 cannot be expressed as a ratio of two whole numbers, which means that it is an irrational number.
ANSWER: The square root of 72 can be classified as an irrational number.
Principal square root of 72
Two square roots exist for every positive number, one being positive and the other negative. The positive root is known as the "principal square root," which is typically used when computing the square root of a number.
In our case, the principal square root of 72 is the positive value of approximately 8.48528, which is written as √72 ≈ 8.48528.
It's worth noting that the positive square root of a positive number is always considered the principal square root. In the case of the square root of 72, both positive and negative numbers multiplied by themselves result in 72. However, we refer to the positive value as the principal square root.
To find the principal square root of 72, we can use a square root calculator or simplify the radical form of the square root of 72 as √(36 x 2). This is because 36 is a perfect square that can be factored out from 72. Hence, we can express the square root of 72 as √36 x √2, which simplifies to 6√2.
Therefore, the principal square root of 72 is 6√2. It should be noted that the square root of 72 is an irrational number, as it cannot be expressed as the quotient of two integers and has an infinite decimal expansion.
In our case, the principal square root of 72 is the positive value of approximately 8.48528, which is written as √72 ≈ 8.48528.
It's worth noting that the positive square root of a positive number is always considered the principal square root. In the case of the square root of 72, both positive and negative numbers multiplied by themselves result in 72. However, we refer to the positive value as the principal square root.
To find the principal square root of 72, we can use a square root calculator or simplify the radical form of the square root of 72 as √(36 x 2). This is because 36 is a perfect square that can be factored out from 72. Hence, we can express the square root of 72 as √36 x √2, which simplifies to 6√2.
Therefore, the principal square root of 72 is 6√2. It should be noted that the square root of 72 is an irrational number, as it cannot be expressed as the quotient of two integers and has an infinite decimal expansion.
