A number’s square root is the worth which, when multiplied by itself, gives the initial number. Let"s explore the simulation below to discover the square root of any number, such together the square source of 89. Once friend grasp the simple concept that square roots, any lesson can be quickly solved.In this lesson, you will learn the square source of 89 and how to find the square root of 89.

You are watching: Square root of 89 simplified radical form

Square source of 89: √89=9.43 (up to 2 decimal place)Square that 89: 89² =7921

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The square root of a number n can be created as √n. It method that over there is a number aa such that a×a=n. This can likewise be created as, a2=n ⇒ a=√n. So, a is equal to the square source of n.Now, if n=89, then a=√89 is the square root of 89. In the radical form, the square source of 89 can be stood for by √89. The square root of 89 = 9.43 in the decimal form up to 2 decimal places. 


A rational number is a number that can be to express in the kind of p/q. A number the is not a reasonable number is dubbed an irrational number. Due to the nature of its non-repeating and also non-terminating decimal expansion, the square root of 89 can not be written in the kind of p/q, hence, it is one irrational number.The value of the square source of 89 in decimal form is 9.433981.. For this reason on, The square source of a number can have two values, a positive and also a negative value. So, √89=+9.433981. Hence, The square root of 89 is an irrational number with never-ending digits.

The long department method helps united state to uncover a much more accurate value of the square root of a number. Let"s watch the steps to find the square root of 89 by the long division method.

Step 1: Divide the number 89 by 9, (because 92 =81 is a perfect square number just less than 89).Step 2: The divisor and also the quotient need to be the very same numbers; in this case, that is 9. Multiply the quotient and also the divisor and also subtract the an outcome from 89.Step 3: For the next divisor, include the ahead divisor v the quotient. (9 + 9 = 18); ar it as the brand-new divisor through a blank on that is right.Step 4: Put a decimal after ~ quotient "9" and bring down two zeros to ar it after 8 so that it i do not care 800. (184 × 4 = 736). Subtract 736 from 800.(800 − 736 = 64)Step 5: Bring down an additional pair of zeros and also place the after 64, so the it i do not care 6400. Take the brand-new quotient 4 and include it to 184. (184 + 4 = 188)Step 6: Repeating the above steps, we have to fill the blank with a number together that once the brand-new divisor is multiplied through the brand-new quotient, the product is much less than or equal to the dividend 6400. (1883 × 3 = 5649)Step 7: write the very same number after ~ 4 in the quotient. Subtract 5649 from 6400. (6400 − 5649 = 751)Step 8: Repeat the procedure until we gain the remainder same to zero. The square root of 89 up to two areas is derived as 9.43 by the long department method.


Explore Square roots making use of illustrations and also interactive examples

Use the hit and also trial method while calculating the square source of any kind of number.The square root of a number deserve to have 2 values.The square source of any number can be assumed in between the square source of two nearest perfect squares of the number. For example, the square source of 89 lies between the square root of 81 and 100. So worth would be better than 9 and also less than 10.
Find the square root of 899 by the approximation method.Find the largest 5-digit number which is a perfect square.

Example 1 Kevin desires to paint the rectangle-shaped floor that his garage. The length of the floor is 10 feet and also the width is √89 feet. Deserve to you assist him find the area that the floor the he has to paint?

Solution Given: Length of the rectangle floor = 10 feet and width that the rectangle floor = √89 feetArea that the floor = Length×WidthArea =10×√89 =10×9.43Area=94.3 feet2

Example 2 Help Tim evaluating √89 × √89.


We recognize that √89 = 9.43399.7339 × 9.4339 = 88.99 ≈ 89on multiplying √89 by √89 we obtain 89.

See more: Convert 57 Kg Equals How Many Pounds And Oz, Convert 57 Kilograms To Pounds

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