Square Root of 60
John loves art and craft, he wants to build a square sheet that has an area of 60 inch^{2}. Now, he wants to measure the side of the square sheet with a ruler so that he can get the exact required area. What do you think he is going to do, is he going to take the square root of 60, to find the sides of the sheet? In this minilesson, we will learn about the square root of 60 by understanding methods to calculate the square root, the long division method to find the square root of any number, and how to apply them while solving problems.
 Square Root of 60: √60= 7.7459666924148
 Square of 60: 60² = 3600
What Is the Square Root of 60?
The square root of any number n can be written as √n. It means then there is a number a such that: a × a = n. Now it can also be written as: a^{2} = n or removing the squares on both the sides, we get a = √n . So, a is called as second root of n.
 Now, if n = 60, then a = √60 is the square root of 60. In the simplest radical form, √60 = √4 x 15 = 2√15
 The decimal form of √60 = 7.74
Is the Square Root of 60 Rational or Irrational?
The square root of 60 is an irrational number with neverending digits. √60 = 7.7459666924148. The square root of 60 can not be written in the form of p/q, hence it is an irrational number.
How to Find the Square Root of 60?
We can find √60 using the method of approximation or using long division method.
Square Root of 60 by Approximation
 Take two perfect square numbers which are just smaller than 60 and just greater than 60.
 √49 = 7 < √60 and √64 = 8 > √60
 7 < √60 < 8
 Multiply the inequality by 10.
 70 < 10 √60 < 80
 √4900 < √6000 <√6400
 Move more closer to the inequality
 √5929 < √6000 < √6084
 77 < 10√60 < 78
 Divide both sides by 10.
 7.7 < √60 < 7.8
 Take the average of both lower and upper limits
 √60 ≈ (7.7 +7.8)/ 2
 √60 ≈ 7.75
Square Root of 60 by Long Division Method
The long division method helps us to find the accurate value of the square root of any number. Let's see how to find the square root of 60 by the long division method.
 Step 1: Find a number such that when we multiply the number by itself the product is less than 60. 7 × 7 = 49
 Step 2: Take the same number as the quotient which is the divisor, 7. multiply the quotient and the divisor and subtract the result from 60
 Step 3: Take the same quotient '7' and add with the divisor '7'.
 Step 4: Apply decimal after quotient '7' and bring down two zeros and place it after 11 so that it becomes 1100. We need to find a new divisor 14X such that the digit placed in X(units place of our new divisor) multiplied to itself gives a number less than 1100, our new dividend. 147 × 7 = 1029. Complete the process of division.
 Step 5: Bring down two zeros again and place it after 71, so that it becomes 7100. Take 7 and add it to 147. 147 + 7 = 154. We need to identify a number X so that when placing it at the end of 154X and multiplying the result with the same number we get a number less than 7100. 1544 × 4 = 6176. Write the same number after 7 in the quotient. Complete the process of division.
 Step 6: Repeat the process to find the square root of 60. The square root of 60 up to two places is obtained by the long division method. is 7.74
Explore Square roots using illustrations and interactive examples
 √60 = √4 × 15 = 2√15
 √60 = + 7.7459666 and √60 =  7.7459666
Challenging Questions:
 Find the square root of 600 up to 3 decimal places by approximation method.
 Find the smallest 6 digit perfect square number.
 Chris wants to find out the value of 12 in terms of a and b,If the value of √√60 = a and √√5= b, help him to pick the correct option.
Square Root of 60 Solved Examples

Example 1: John, a salesman wants to build a rectangular floor garage to store goods for his shop. He wants the floor of length 20 feet and width of 10√60 feet, if he wants to paint the floor at $2 per square feet, how much money he has to pay.
Solution:
Length of the rectangle floor = 20 feet
Width of the rectangle floor = 10√60 feet
Area of the floor will be length x breadth sq feet
20 × 10√60 = 200√60
= 200 × 7.745
= 1549 sq feetCost of painting the floor = $2 per sq feet
Total Cost = 1549 × 2= $3098Therefore, John has to pay $3048

Example 2: A car is traveling at a speed of 6√240 miles/hr, how much distance will it cover in 2 hours?
Solution:
Speed of the car = 6√240 miles/hr
Time = 2 hours
Applying speed formula:Speed = Distance/Time
6√240= Distance / 2
Distance = 6 √240 × 2
=12 √(4 × 60)
=12 × 2 √60
=24 √60
= 24 × 7.745
185.88 miles
Therefore, the car will cover 185.88 miles.
FAQs On Square Root of 60
What is the square root of 60?
The square root of 60 is √60 = 2 √15 = 7.7459
Is square root of 60 a rational number?
The square root of 60 is not a rational number because we can not express√60 in the form of p/q due to its nonterminating and nonrepeating nature of decimal form. √60 is irrational.
Is 60 a perfect square?
60 is not a perfect square. √60 = 2 √15, and cannot be expressed as n^{2}
How do you find the square root of 60?
Find the two perfect square numbers between which 60 lies. We know it lies between 49 and 64. So the √60 lies between √49 and √64, i.e between 7 and 8. Then the approximate value of √60 is evalulated.
What is the radical form of √60?
The radical form of √60 is 2√15.