Square Root of 85
Did you know that 85 is the product of two distinct prime numbers, 5 and 17? In this lesson, we will learn that √85 is a non-terminating, non-repeating decimal. The square root of 85 is written as √85. We call this a representation of square root of 85 in radical form. 85 can be called a perfect square only if the square root of 85 gives a perfect whole number. Let us see how to find the square root of 85 and check whether 85 is a perfect square or not.
- Square Root of 85: √85 = 9.219544
- Square of 85: 852 = 7225
|1.||What Is the Square Root of 85?|
|2.||Is Square Root of 85 Rational or Irrational?|
|3.||How to Find the Square Root of 85?|
|5.||FAQs on Square Root of 85|
What Is the Square Root of 85?
The square root of a number is the number which, when multiplied to itself, gives the original number. The square root of 85 is 9.21 and is shown as √85 = 9.21. The value of the square root of 85 lies between the whole numbers 9 and 10.
Is the Square Root of 85 Rational or Irrational?
The square root of 85 is a non-terminating decimal, i.e., √85 = 9.219544. Also, it cannot be expressed in the form of a fraction p/q, and hence, it is an irrational number.
How to Find the Square Root of 85?
The number 85 is not a perfect square, so its value can be approximated between 9 and 10. √85 = 9.21. The exact value of the square root of 85 can be calculated using long division. This method to find the square root of 85 is similar to the normal division, where the quotient represents the square root value. Further, since 85 is not a perfect square, the remainder is never 0 and the division process is concluded after a few steps.
Square Root of 85 By Long Division
The square root of 85 can be found by the following long division method. Let's see the steps to find the square root of 85 by the long division method.
- Step 1: Divide the number 85 by 9, because 9² = 81 is a perfect square number that is less than 85.
- Step 2: The divisor and the quotient need to be the same numbers; in this case, it is 9. Multiply the quotient and the divisor and subtract the result 81 from 85.
- Step 3: For the next divisor, add the previous divisor with the quotient. (9 + 9 = 18); place it as the new divisor with a blank on its right.
- Step 4: Put a decimal after quotient 9 and bring down two zeros to place it after 4 so that it becomes 400. The blank needs to be filled with a number, such that when the new divisor is multiplied with the new quotient, the product is less than or equal to the dividend. [182 × 2 = 364] Subtract 364 from 400 [400 - 364 = 36].
- Step 5: Bring down two zeros again and place it after 36, so that it becomes 3600. Take the new quotient 2 and add it to 182 [182 + 2 = 184]. Repeating the above steps, we need to fill the blank with a number such that when the new divisor is multiplied with the new quotient, the product is less than or equal to the dividend 3600.
- Step 6: Repeat the process till we get the remainder equal to zero. This is how the square root of 85 up to two places is obtained by the long division method.
Explore square roots using illustrations and interactive examples
- Find the square root of √8585
- Simplify (((√85)½)¾)
Square Root of 85 Solved Examples
Example 1: Jack needs to cut a square-shaped cardboard for his school assignment. The required area of the cardboard is 85 square inches. Can you help Jack find the length of each side of the cardboard?
Given that the area of the cardboard is 85 square inches.
Area of the square = x²
Let's calculate the value of x.
x² = 85
x = √85
x = 9.2
Thus, the length of each side of the cardboard is 9.2 inches.
A cultural club was formed and the members decided to collect an annual subscription fee. The annual subscription fee equals the total number of members in the club. If the total subscription fee collected is $7225, find the number of members in the club.
Given that the number of members in the club is equal to the value of the subscription amount per member.
Let the number of members in the club = Subscription per member = x
Total subscription received = $7225
Number of members X subscription per member = $7225
x × x = 7225
x² = 7225
x = √7225
x = √(85 × 85)
x = 85
Thus, the subscription per member is $85.
FAQs on Square Root of 85
What is the square root of 85?
Square root of 85 is √85 = 9.219544
What is the square of 85?
Square of 85 is 852 = 7225
How do you work out the square root of 85?
We can find the square root of 85 using various methods.
- Repeated Subtraction
- Prime Factorization
- Estimation and Approximation
- Long Division
If you want to learn more about each of these methods, click here.
What is the value of √85 times √85?
√85 × √85 = 85.
What is the square root of 85 in the simplest radical form?
√85 is the simplest radical form.
Is the square root of 85 an irrational number?
√85 = 9.219544
Thus, √85 is an irrational number.