How to Calculate the Square Root of 5 with Detailed Examples
The value of root 5, when reduced to 5 decimal points, is √5 = 2.23606. It has a place with a large list of irrational algebraic numbers. It has been sorted in light because of the fact that the square root of 5 can't be described as a fraction and has an eternal number of decimals. Additionally, the specific value can never be found perfectly. In Mathematics, the square root of 5 is presented or written as √5. It is a positive number and also the value of √5 when multiplied by itself, gives you the prime number 5. To distinguish itself from a negative number with the same properties, it is called as the principal root of 5.
How to Find the Square Root of 5?
This question might be bothering you for quite some time now. The simplest way to find the square root of any number would be by using the division method. How to find the value of root 5? Follow the steps given below:
Step 1: The first step is to group the digits in pairs of two. You start from the unit that is in the unit place and move towards the left-hand side for a number before the decimal point. For the number after the decimal point, you group the first two numbers and move towards the right-hand side.
5. 00 00 00 00
Step 2: In this step, you will have to pick the largest square number that is either equal to or lesser than the first number pair. Now take this number as the divisor and also note down the quotient.
Step 3: Now, you subtract the final product of the quotient and the divisor and the quotient from the pair of numbers or the number. Next, you bring down the next pair of numbers.
Step 4: You now need to calculate the divisor. To do that, you’ll have to multiply the previous quotient by 2 and then pick a new number in such a way that the digit and the new divisor is less than or equal to the new dividend
Step 5: Repeat Step 2, Step 3, and Step 4, until all the pairs of numbers are exhausted. Now, the quotient that you’ve found is the square root. In case of the value of under root 5, this is how it is done.
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Therefore, the square root of 5 = 2.236
What is the Square Root of 5?
The value of root 5, when reduced to 5 decimal points, is 2.23606 and this is just the simplified version of the value. In addition to that, the actual value of root 5 can be equal to at least ten billion digits.
Sample Questions
1. Using the division method, find the square root of the value 784.
Solution:
2. Using the division method, find the square root of the value 5329
Solution:
3. Find the square root of 66049
Solution:
Did you know?
5 is not a perfect square as the square root of 5 is not a whole number.
The square root of 5 in exponential form can be written as (5)½ or (5)0.5.
When solving a problem having a square root of 5 it is advisable to take the value till 3 decimal points.
Is the square root of the number 5 a rational number or an irrational number?
First let us understand what rational and irrational numbers are. A rational number is a number that can be written in the form of a ratio between any two integer numbers. For example, the square root of 9 is equal to 3, which can also be written as 3/1.
Whereas, an irrational number is a number that can not be written in the form of a ratio between any two integer numbers. So, the square root of 5 which is equivalent to 2.23 up to its two decimal values, which is an irrational number.
Solved examples
1. Suppose the sides of a square photo frame is 2.33 m in length. Find out the area of the photo frame and write the answer to its nearest roundoff.
Ans. Length of the side of the photo frame= 2.33 m
Area of square = (side)2
Substituting the value of the length to the above equation we get,
Area of photo frame= (2.33)2= 5.4289m2
Rounding it off we get 5 m2
2. The area of a square-shaped wall is 25m2. What is the length of one side of the wall? What is the perimeter of the wall?
Ans. Area of square = (side)2
Substituting the value of the area of the wall we get,
25 = (side)2
√25 = side = 5 meters.
Perimeter of square = 4 x side
= 4 x 5 = 20 meters.
3. What is the value of 15√5?
Ans. 15√5 = 15 x 2.236 = 33.54101
4. Evaluate the following problems:
1. 5√16+2√25-2√5
2. √5 - √1
3. 20√25 - 10√9 - 5√5
Ans.
1. 5√16+2√25-2√5
= (5 x 4) + (2 x 5) + (2 x 2.236)
= 20 + 10 + 4.472
= 34.472
2. √5 - √1
= 2.236 – 1
= 1.236
3.20√25 - 10√9 - 5√5
= (20 x 5) – (10 x 3) – (5 x 2.236)
= 100 – 30 – 11.18
= 58.82
Refer to the solved examples to understand how the concept of the square root of 5 has been used. Learn how it is defined and calculated to get a better idea of this topic. By doing this, you can easily find out the square roots of other whole numbers easily.
FAQs on Square Root of 5: Value & Calculation Methods
1. What exactly is the square root of 5?
The square root of 5, represented by the symbol √5, is a positive real number that, when multiplied by itself, gives the number 5. Since 5 is not a perfect square, its square root is an irrational number, meaning its decimal representation never ends and does not repeat. For practical calculations, its value is often approximated to 2.236.
2. Is the square root of 5 a rational or irrational number, and why is this important?
The square root of 5 is an irrational number. This is important because it cannot be expressed as a simple fraction (a/b, where a and b are integers). Understanding this property is fundamental in number theory and algebra, as it helps classify different types of real numbers and their behaviour in mathematical operations. For example, knowing √5 is irrational confirms it cannot be simplified to a whole number or a terminating decimal.
3. How can we find an approximate value for the square root of 5 using the long division method?
The long division method is a step-by-step process taught in the CBSE syllabus to find the value of square roots. Here is a simplified overview of the steps:
- Step 1: Place a bar over the digit 5 and pair the zeros after the decimal point (5.00 00 00).
- Step 2: Find the largest number whose square is less than or equal to 5. This is 2 (since 2²=4).
- Step 3: Bring down the next pair (00) to make the new dividend. Double the quotient (2) to get 4, which becomes the new divisor's tens digit.
- Step 4: Find a digit 'x' such that 4x multiplied by x is less than or equal to the new dividend.
- Step 5: Repeat the process to get the value to the desired number of decimal places, which is approximately 2.236.
4. What is the key difference between finding the square root of 5 and the square root of 25?
The key difference lies in the nature of the numbers. 25 is a perfect square (5 × 5 = 25), so its square root is a whole number (an integer), which is 5. In contrast, 5 is a non-perfect square. Its square root, √5, is an irrational number (approx. 2.236) that cannot be simplified to a whole number or a simple fraction. This distinction is a core concept in understanding number systems.
5. Can the square root of 5 be simplified further from its radical form (√5)?
No, the radical form √5 is its simplest form. Simplification of a square root involves factoring out any perfect square factors from under the radical sign. For instance, √20 can be simplified to √(4 × 5) = 2√5. Since the number 5 is a prime number, it has no perfect square factors other than 1. Therefore, √5 cannot be broken down or simplified any further.
6. Where might we see the importance or application of the square root of 5 in mathematics?
The square root of 5 is not just an abstract number; it has significant applications in geometry and advanced mathematics. A primary example is its connection to the Golden Ratio (φ), which is (1 + √5) / 2. The Golden Ratio appears frequently in geometry, art, architecture, and nature. Therefore, understanding √5 is crucial for exploring concepts related to proportion and geometric harmony as per the NCERT curriculum.
7. How is the concept of a 'square root' generally defined in maths?
In mathematics, the square root of a number 'x' is defined as a value 'y' such that y² = x. In other words, it is a number that, when multiplied by itself, results in the original number. Every positive number has two square roots: one positive (the principal root) and one negative. For example, the square roots of 9 are +3 and -3. The symbol '√' is used to denote the principal (positive) square root.
