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Square Root of 5 is a positive real number that when multiplied by itself gives the number 5. The square root of 5 is 2.2360679. It is expressed as √5 in radical form, and as (5)½ or (5)0.5 in the exponent form. 5 is not a perfect square as the square root of 5 is not a whole number. The square root of 5 is the positive solution of the equation x2 = 5.
- Square Root of 5: 2.23606797749979
- Square Root of 5 in Radical Form: √5
- Square Root of 5 in Exponential Form: (5)½ or (5)0.5
Read More: NCERT Solutions for Class 8 Mathematics Squares and Square Roots
Key Terms: Square Root of 5, Square Root, Perfect Square, Multiplication, Long Division, Whole Number, Prime Factorization
What is Square Root of 5?
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Square Root of a number is the number that can be multiplied by itself to obtain a given number. The square root of the number 5 is not a whole number as 5 is not a perfect square number.
| √5 = 2.23607 |
The square root of 5 cannot be expressed as a fraction and is expressed in the form of infinite decimals. The square root of √5, shortened to 50 decimal places is given as
| √5 = 2.23606797749978969640917366873127623544061835961152… |
Is Square Root of 5 Rational or Irrational?
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Square Root of 5 is around 2.23606797749979.
- A rational number is one that can be written as the ratio of two numbers, p/q where q is not equal to 0.
- An irrational number is one that cannot be represented by the ratio of two numbers.
The square root of 5 has an infinite number of decimal places. Thus, it cannot be expressed in the p/q form. It implies that 5 is not a perfect square.
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How to Find Square Root of 5?
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Square Root of a number can be easily calculated using the Prime Factorization method. However, when the given number is not a perfect square, we need to use the Long Division method to find the exact value of the square root of the number.
Square Root of 5 can be calculated using the given two methods:
- Prime Factorization
- Long Division
Square Roots of non-perfect squares are irrational and has an infinite value which is then rounded off to the nearest to get an estimated value.
Read More: Estimating Square Root
Square Root of 5 Using Prime Factorization
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Since 5 is a prime number, the prime factorization of 5 is given as
5 = 5 × 1
5 = 5
Taking square root, we get
√5 = √5
√5 = 2.23
Thus, the square root of 5 is approximately 2.23.
Square Root of 5 Using Long Division
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The steps to find out the square root of 5 by using the long division method are as follows:
- Step 1: First, the digits should be paired in a group of 2, starting from the unit place and moving from right to left before the decimal point with a bar over them.
- Step 2: Find the largest number whose product is less than or equal to 5 on multiplication with itself. As 2 × 2 = 4 and is less than 5, we will divide 5 by 2
- Step 3: Put a decimal point and pairs of zeros and continue the division.
- Step 4: Multiply the quotient by 2 and the product becomes the starting digit of the next divisor.
- Step 5: Now, find a number in the unit's place for the new divisor such that its product with a number is less than or equal to 100. Taking 2 as the number, we will get 42 × 2 = 84.
![square root of 5 by factor]()
- Step 6: Take down the next pair of zeros and multiply the quotient 22 by 2, which is 44 and this becomes the starting digit of the new divisor.
- Step 7: In the same manner as the last one, find a number in the unit's place for the new divisor such that its product with a number is less than or equal to 1600.
- Step 8: It can be seen that 443, when multiplied by 3, gives 1329 which is less than 1600.
- Step 9: Now, continue taking down the pair of zeros and repeating the same process.
The division process will be never-ending, thus, the square root of 5 is an irrational number. Hence, the value of the square root of 5 is 2.236.
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Solved Examples on Square Root of 5
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Here are a few solved problems on the square root of 5:
| Example 1: Find the value of 3 square root 5. Solution: According to the question, 3√5 =? We know that the square root of 5 is 2.236. Substituting the values, we get 3√5 = 3 × 2.236 = 6.708 Thus, the value of 3 square root 5 is 6.708. Example 2: The area of a square-shaped poster is 25m2. What is the perimeter of the poster? Solution: The area of a square is given as Area of Square = (Side)2 Substituting the value of the area of the poster we get, 25 = (Side)2 √25 = 5 meters The perimeter of the square-shaped poster = 4 x Side Perimeter = 4 x 5 = 20 meters. |
Read More: Squares and Square Roots MCQs
Things to Remember
- Square Root of 5 is the number which when multiplied by itself twice, gives 5 as the product.
- The square root of 5 is 2.236.
- It is expressed as √5 in radical form and (5)½ or (5)0.5 in the exponent form.
- The square root of 5 is an irrational number as its value has an infinite number of decimal places.
- 5 is not a perfect Square as its square root is not a whole number.
- The estimated value of the square root of 5 can be found using the long division method.
Sample Questions
Ques. Evaluate the given expressions:
1. 5√16 + 2√25 - 2√5
2. √5 - √1
3.20√25 - 10√9 - 5√5 (3 Marks)
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
Ques. The area of a square-shaped box is 25m2. Find the length of the side of the box. (2 Marks)
Ans. We know that
Area of a Square = Side × Side = Side2
Side = √25 = 5
Thus, the side length of the bed is 5 m.
Ques. Find out the value of 15√5. (2 Marks)
Ans. The approximate value of √5 is 2.236.
Substituting the values, we get
15√5 = 15 x 2.236 = 33.54101
Thus, the value of 15√5 is 33.54101.
Ques. What is the Square Root of 5? (1 Mark)
Ans. The square root of 5 is around 2.23606. The value of the square root of 5 is infinite and is rounded to its nearest value.
Ques. Suppose the sides of a square are 2.33 m in length. Find the area of the square and find the answer to its nearest roundoff. (2 Marks)
Ans. The length of the side of the square is given as 2.33 m.
Area of Square = (Side)2
Substituting the value of the length to the above equation we get,
Area of Square= (2.33)2 = 5.4289m2
Rounding off the value, we get the area of the square as 5 m2.
Ques. How to prove that the square root of 5 is an irrational number and the square root of 25 is a rational number? (2 Marks)
Ans. We know that
- Square Root of 25 = 5
- Square Root of 5 = 2.236
The square root of 25 is rational since it is a whole number. On the other hand, the square root of 5 is around 2.236 on rounding off. Its value is infinite, thus, it is irrational.
Ques. Why is the square root of 5 an Irrational number? (2 Marks)
Ans. When the square root of 5 is calculated using the long division method, its value is given as around 2.23606797749979. The value of the square root of 5 is never-ending and is thus infinite. Thus, the square root of 5 is an irrational number.
Ques. What is the Square Root of -5? (2 Marks)
Ans. There is no real number equal to -5's square root. It is known as the imaginary unit and can be represented as √-5 = √-1 × √5 = i √5 = 2.236i, where i = √-1 and is an imaginary unit.
Ques. What will be the value of 12 plus 15 square root 5? (2 Marks)
Ans. According to the question,
12 + 15√5
We know that the square root of 5 is 2.236. Thus,
12 + 15 x√5 = 12 + 15 x 2.236 = 12 + 33.541 = 45.541.
Thus, the value of 12 plus 15 square root 5 is 45.541.
Ques. What is the simplest radical form of the square root of 5? (2 Marks)
Ans. The number 5 is a prime number which means it is only divisible by 1 and itself. It means number 5 does not have a pair and is not in the power of 2. Thus, the radical form of the square root of 5 cannot be simplified further.
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