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 number is √5?
The square root of 5, denoted as $\sqrt{5}$, is an irrational number. Its approximate decimal value is $\sqrt{5} \approx 2.236$. This value cannot be exactly represented as a fraction, and its decimal expansion is non-repeating and non-terminating. At Vedantu, students can learn how to calculate and estimate square roots for different numbers through guided explanations and interactive sessions.
2. What is the square root of ✓ 5?
The symbol ✓ 5 refers to the square root of 5.
- Mathematically, $\sqrt{5} \approx 2.236067977$
- This value is useful in geometry and algebra, especially in calculations involving certain triangles and the golden ratio.
3. How to calculate a square root?
To calculate a square root:
- For perfect squares (e.g., 4, 9, 16), simply find a number which, when multiplied by itself, gives the original number.
- For non-perfect squares like 5, use methods such as:
- Prime factorization (if possible)
- Long division method for manual calculation
- Estimation and approximation techniques
Vedantu offers step-by-step lessons and video tutorials for each method, ensuring students gain strong foundational skills in square root calculations.
4. What is the square of a 5?
The square of 5 is calculated as $5^2$.
- $5 \times 5 = 25$
Squaring a number means multiplying the number by itself, a concept explained thoroughly in Vedantu’s interactive math courses.
5. What is the value of root 5 in decimal up to 5 places?
The value of $\sqrt{5}$ in decimal form up to five decimal places is:
- $\sqrt{5} = 2.23606$ (rounded to five decimal places)
Understanding how to approximate square roots is part of Vedantu’s comprehensive mathematics curriculum, supported by expert-led live sessions.
6. Is the square root of 5 a rational or irrational number?
The square root of 5, or $\sqrt{5}$, is an irrational number. This means it cannot be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. Its decimal expansion does not repeat or terminate. Vedantu’s educators help students clearly distinguish between rational and irrational numbers through systematic explanations.
7. How to simplify expressions involving √5?
To simplify expressions with $\sqrt{5}$:
- Combine like terms, e.g., $2\sqrt{5} + 3\sqrt{5} = 5\sqrt{5}$.
- Rationalize denominators: $\frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5}$.
Vedantu provides practice problems and detailed solutions to help students master simplification techniques using square roots and other surds.
8. What is the significance of root 5 in geometry?
The square root of 5 appears in several geometric contexts, including:
- Diagonal of a rectangle: In a $2 \times 1$ rectangle, the diagonal length is $\sqrt{5}$.
- Pentagon geometry: The golden ratio involves $\sqrt{5}$.
Students on Vedantu learn about such real-world and geometric applications of square roots through interactive visuals and problem-solving sessions.
9. Can √5 be located exactly on a number line?
$\sqrt{5}$ cannot be represented as a precise point using rational coordinates but its approximate position can be constructed:
- Draw a segment of length 2 units and another of 1 unit on a straight line to form a right triangle. By the Pythagorean theorem, the hypotenuse will have length $\sqrt{5}$.
Vedantu’s teaching modules explain and demonstrate methods to represent surds like $\sqrt{5}$ on a number line using geometric constructions.
