The square source of 85 is expressed as √85 in the radical kind and together (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 hopeful solution of the equation x2 = 85.

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

The square root of a number is the number which, whenmultiplied come itself, offers the original number. The square source of 85 is 9.21 and is presented as√85 = 9.21. The worth of the square source of 85 lies between the whole numbers 9 and also 10.


The square source of 85 is a non-terminating decimal, i.e., √85 = 9.219544.Also, it can not be to express in the form of a fraction p/q, and also hence, the is one irrational number.


The number 85 is not a perfect square, for this reason its valuecan be approximatedbetween 9 and also 10. √85 = 9.21. The exact value of the square root of 85 have the right to be calculated using long division. This technique to uncover the square source of 85 is similar to the typical division, wherein the quotient represents the square root value. Further, since 85 is no a perfect square, the remainder is never 0 and the division process is concludedafter a few steps.

Square source of 85ByLong Division

The square source of 85 have the right to be discovered by the adhering to long department method. Let's check out the steps to uncover the square root of 85 by the long division method.

Step 3:For the next divisor, include the ahead divisor through the quotient. (9 + 9 = 18); place it as the brand-new divisor through a blank on its right.Step 4:Put a decimal after quotient 9andbring down 2 zeros to location it ~ 4 so the it becomes 400.The empty needs to be filled v a number, together that when the new divisor is multiplied through the new quotient, the product is less than or equal to the dividend. <182 × 2 = 364> Subtract 364 indigenous 400 <400 - 364 = 36>.Step 5:Bring down 2 zeros again and also place the after 36, so the it i do not care 3600. Take it the new quotient 2 and include it to 182 <182 + 2 = 184>. Repeating the above steps, we must fill the blank with a number such that when the brand-new divisor is multiplied v the new quotient, the product is less than or equal to the dividend 3600.Step 6:Repeat the procedure till we obtain the remainder same to zero. This is how the square source of 85 up to two places is derived by the long department method.

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Explore square roots using illustrations and also interactive examples


Challenging Questions:


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

Square root of 85Solved Examples


Example 1:Jack requirements to cut a square-shaped cardboard because that his institution assignment. The compelled area that the cardboard is 85 square inches. Have the right to you assist Jack uncover the size of every side the the cardboard?

Solution

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


Example 2

A cultural club to be formed and also the members decided to collect an yearly subscription fee. The yearly subscription fee equalsthe total variety of members in the club. If the full subscription fee gathered is $7225, discover the variety of members in the club.

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Solution:

Given the the number of members in the society is same to the value of the subscription amount every member.Let the variety of members in the club = Subscription per member = xTotal subscription received = $7225Number that members X subscription per member = $7225x × x = 7225x² = 7225x = √7225x = √(85 × 85)x = 85Thus, thesubscription per member is $85.