Square Root of 60
The square root of 60 is expressed as √60 in the radical form and as (60)^{½} or (60)^{0.5} in the exponent form. The square root of 60 rounded up to 10 decimal places is 7.7459666924. It is the positive solution of the equation x^{2} = 60. We can express the square root of 60 in its lowest radical form as 2 √15.
 Square Root of 60: 7.745966692414834
 Square Root of 60 in exponential form: (60)^{½} or (60)^{0.5}
 Square Root of 60 in radical form: √60 or 2 √15
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. 
Example: If the area of an equilateral triangle is 60√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 60√3 in^{2}
⇒ a = ±√240 in
Since length can't be negative,
⇒ a = √240 = 2 √60
We know that the square root of 60 is 7.746.
⇒ a = 15.492 in
FAQs on the Square Root of 60
What is the Value of the Square Root of 60?
The square root of 60 is 7.74596.
Why is the Square Root of 60 an Irrational Number?
Upon prime factorizing 60 i.e. 2^{2} × 3^{1} × 5^{1}, 3 is in odd power. Therefore, the square root of 60 is irrational.
What is the Square Root of 60 in Simplest Radical Form?
We need to express 60 as the product of its prime factors i.e. 60 = 2 × 2 × 3 × 5. Therefore, √60 = √2 × 2 × 3 × 5 = 2 √15. Thus, the square root of 60 in the lowest radical form is 2 √15.
Evaluate 8 plus 9 square root 60
The given expression is 8 + 9 √60. We know that the square root of 60 is 7.746. Therefore, 8 + 9 √60 = 8 + 9 × 7.746 = 8 + 69.714 = 77.714
What is the Square of the Square Root of 60?
The square of the square root of 60 is the number 60 itself i.e. (√60)^{2} = (60)^{2/2} = 60.
What is the Value of 15 square root 60?
The square root of 60 is 7.746. Therefore, 15 √60 = 15 × 7.746 = 116.190.
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