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Square Root of 3 is a number that when multiplied by itself, results in the original number 3. The value of the square root of 3 is 1.7320508. It is expressed as √3 in its radical form and as (3)½ or (3)0.5 in the exponential form. The square root of 3 is an irrational number as it is infinite and not a whole number. Thus, 3 is not a perfect square number. The square root of 3 is the positive solution of the equation x2 = 3. The method of long division is used to calculate the square root of 3.
Read More: NCERT Solutions for Class 8 Mathematics Squares and Square Roots
Key Terms: Square Root of 3, Square Root, Irrational Number, Whole Number, Multiplication, Long Division, Prime Factorization
What is Square Root of 3?
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Square Root of 3 is the value that gives the original number 3 on multiplication with itself. The square root of 3 is irrational, i.e. it is never-ending.
√3 = 1.7320508075688772
Square Root of 3 is expressed as follows in various forms:
| Form | Representation |
|---|---|
| Decimal | 1.732 |
| Radical | √3 |
| Exponential | 30.5 or (3)½ |
Is Square Root of 3 Rational or Irrational?
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In a rational number, the decimal part terminates, i.e. it is finite, whereas, in an irrational number, the decimal part is non-terminating. We know that
√3 = 1.73205080…...
It can be seen that the decimal part of √3 is non-terminating, i.e., unending. Hence, the square root of 3 is an irrational number.
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How to Find Square Root of 3?
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Square Root of 3 is an irrational number, thus, it cannot be calculated using prime factorization. Thus, it can be calculated using the long-division method.
The steps to find the square root of 3 using the long division method are as follows:
- Put a decimal after and write zeros in pairs of two starting from the left of the decimal to the right.
- Now see which number is equal to or less than 3 when multiplied by itself. It is number 1. So, write 1 as the divisor and set 1 as the quotient.
- The remainder becomes 2 after subtracting 1 from 3.
- Bring a pair of zeros next to the decimal down so that the dividend becomes 200. Also, add the divisor to itself, i.e., 1 + 1.
- Now, the divisor will become 2x, in which the value of x should be equal to or less than 200. 27 fits the best as the value of Y.
- Put a decimal after 1 in the quotient and then write 7.
- The new divisor will be 27 + 7, which is 34 in this case.
![How to Find Square Root of 3]()
Proceed in the same manner repeating from step 4, to calculate the value of the square root of 3.
Thus, the square root of 3 is approximately 1.7320508.
Read More: Finding Square Root Through Repetitive Subtraction
Solved Examples on Square Root of 3
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| Example 1: Shyam is traveling down the highway in the car at an average speed of 10√3 km/hr. If the time taken during this is exactly 1 hour, then calculate the covered distance. Solution: To calculate the covered distance, we have to use the formula: Distance = Speed x Time
Substituting the values of time and speed in the formula, Distance= 17.32 x 1= 17.32 Km So, the total distance covered by Shya is 17.32 Km. Example 2: Write a Pythagorean triplet using √3. Solution: The way to find a Pythagorean triplet of any real number m is 2m, m2+1, m2-1. Putting the value of m in each, the triplet is as follows:
Thus, the Pythagorean triplets are 2√3, 4, and 2. |
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Square Root 1 to 25
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The value of the square root of the number 1 to 25.
| Number | Square Root (√) |
|---|---|
| 1 | 1 |
| 2 | 1.414 |
| 3 | 1.732 |
| 4 | 2 |
| 5 | 2.236 |
| 6 | 2.449 |
| 7 | 2.646 |
| 8 | 2.828 |
| 9 | 3 |
| 10 | 3.162 |
| 11 | 3.317 |
| 12 | 3.464 |
| 13 | 3.606 |
| 14 | 3.742 |
| 15 | 3.873 |
| 16 | 4 |
| 17 | 4.123 |
| 18 | 4.243 |
| 19 | 4.359 |
| 20 | 4.472 |
| 21 | 4.583 |
| 22 | 4.69 |
| 23 | 4.796 |
| 24 | 4.899 |
| 25 | 5 |
Read More: Cube Root 1 to 20
Things to Remember
- Square Root of 3 is a number that gives 3 as the product when multiplied by itself.
- The value of the square root of 3 is 1.732.
- It is expressed as √3 in its radical form and (3)½ or (3)0.5 in exponential form.
- The square root of 3 is an irrational number as its value is never-ending.
- 3 is a non-perfect square, thus, its square root is determined using the long division method.
- The value of √3 is a real number.
Sample Questions
Ques. A bus has to drop its passenger at the final stop, which is 50√3 Km away. It will take 2 hours to complete this journey. Calculate how fast the speed of the bus is. (2 Marks)
Ans. The given distance is 50√3 Km.
Value of √3 = 1.732
- Total Distance = 50√3 = 50 x 1.732 = 86.603 Km
- Time Taken = 2 Hours
Speed = Distance/Time
Speed = 86.603 / 2 = 43.30 Km/hr
Thus, the speed of the bus is the 43.30 Km/hr.
Ques. Is Square root 3 a real number? (2 Marks)
Ans. The square root of 3 is an irrational number as its decimal part is non-terminating. However, it is to be noted that both rational and irrational numbers are real numbers. Hence, even though the square root of 3 is an irrational number, it still falls under the category of real numbers.
Ques. Explain how the square root of 3 is not a rational number. (2 Marks)
Ans. The rational number is simply defined as a number having terminating decimals. This means they can be written in a ratio/fraction. But in the case of √3, the value of it is unending, that is, it continues beyond this number 1.732050807…. Hence, cannot be written in the form of a fraction/ratio.
Ques. Solve 52 + 64 x 31/2. (2 Marks)
Ans. We know that
- Square of 5 = 25
- Value of 31/2 = 1.732
Substituting the values, we get
25 + 64 x 1.732
= 25 + 110.848
= 135.848
Ques. What is the value of the Square Root of 3?
a. 1.7232
b. 1.7320
c. 1.733
d. 1.7322 (1 Mark)
Ans. (b) 1.7320
Explanation: Through the long division method, the correct value of the square root of 3 is determined as 1.7320 approximately.
Ques. Evaluate the value of 19 x 20√3 + 100. (2 Marks)
Ans. The value of the square root of √3 is 1.7320 approximately.
Substituting the value, we get
(19 x 20 x 1.7320) + 100
= 658.16 + 100
= 758.16
Thus, the value of 19 x 20√3 + 100 is 758.16 .
Ques. Find the value of 1.732√3. (1 Mark)
Ans. The value of √3 is 1.732. Thus, the square of 1.732 will be the solution to the given question. Hence, the answer is 2.999824
Ques. Is it possible to find the exact decimal value of the square root of 3? (2 Marks)
Ans. As √3 is a non-perfect square and is an irrational number, there is no end to the digits after the decimals. Hence, it is 1.7320508075688772935274463415058…. However, for an approximate number, it is considered as 1.723.
Ques. Find 50% of square root 3. (2 Marks)
Ans. According to the question,
50% x √3
- The approximate value of square root 3 is 1.732.
- 50% is equal to 0.5 or ½.
1.732 / 2 = 0.866
Thus, 50% of square root 3 is 0.866.
Ques. Calculate the distance traveled by Ravi if he covers the journey from Kota to Jaipur in 6 hours. The speed of his car is 80√3 km/hr. (2 Marks)
Ans. We know that
Distance = Speed X Time
Time Taken = 6 Hours
Speed = 80√3 = 138.56 (As the value of √3= 1.732)
Hence, the distance traveled in 6 hours is 138.56 x 6 = 831.36 Km.
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