The square root of 85 is expressed as √85 in the radical form and as (85)½ or (85)0.5 in the exponent form. The square root of 85 rounded up to 10 decimal places is 9.2195444573. It is the positive solution of the equation x2 = 85.

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Square Root of 85: 9.219544457292887Square Root of 85 in exponential form: (85)½ or (85)0.5Square Root of 85 in radical form: √85
1.What Is the Square Root of 85?
2.IsSquare Root of 85Rational or Irrational?
3.How to Find the Square Root of 85?
4.Challenging Questions
5.FAQs on Square Root of 85

The square root of a number is the number which, whenmultiplied 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.


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.


The number 85 is not a perfect square, so its valuecan be approximatedbetween 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 concludedafter a few steps.

Square Root of 85ByLong 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 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 9andbring 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.

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Explore square roots using illustrations and interactive examples


Challenging Questions:


Find the square root of√8585Simplify (((√85)½)¾)

Square Root of 85Solved 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?

Solution

Given that the area of the cardboard is 85 square inches.Area of the square =x²Let's calculatethe value of x.x² = 85x = √85x = 9.2Thus, the length of each side of the cardboard is 9.2 inches.


Example 2

A cultural club was formed and the members decided to collect an annual subscription fee. The annual subscription fee equalsthe total number of members in the club. If the total subscription fee collected is $7225, find the number of members in the club.

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Solution:

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 = xTotal subscription received = $7225Number of members X subscription per member = $7225x × x = 7225x² = 7225x = √7225x = √(85 × 85)x = 85Thus, thesubscription per member is $85.