The square root of 128 is a number which when multiplied through itself, results in the number 128. The value of a square root deserve to be a decimal or a whole number, or one integer. Us will currently look at just how to calculate the square root of 128 and see a few interesting problems.128 is additionally represented together 27. In this lesson, we will calculate the square root of 128 through long division method.

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Square root of 128: √128 = 11.313Square of 128: 128² = 16,384
1.What Is the Square root of 128?
2.Is Square source of 128 rational or Irrational?
3.How to find the Square source of 128?
4.Tips and also Tricks
5.FAQs top top Square root of 128
6.Important note on Square source of 128

The square source of a number is the number that when multiplied to itself gives the original number as the product. I.e. A × a = n and also it is a2 = n. Recognize square source is the inverse procedure of squaring a number. Therefore, a = n

Radical form: 128 = 27 = 2 × 2 × 2 × 2 × 2 × 2 × 2 ⇒ 128 = (2 × 2 × 2 × 2 × 2 × 2 × 2 ) = 2 × 2 × 2 × 2 = 8 2Exponential form: 128½Approximate value : 11.313

The square source of 128 deserve to be calculated using different methods such as prime factorization or the long department method or the approximation method.

Square source of 128 by Approximation Method

128 lies between the two perfect squares 121 and 144. 121 121 11 now divide 128 by 11 or 12. Let us divide by 11. 128 ÷ 11 = 11.63Find the average of the quotient so acquired with 11. (11.63 + 11) ÷ 2 = 22.63 ÷ 2 = 11.315128 ≈ 11.315

Square root of 128 through Long division Method

Step 1: compose 128 together 128000000. Pick the number in bag from the right. We have actually 1 alone in the left.Divide 1 by 1 and also get the remainder 0. Quotient is 1. Carry down the next pair, 28. 28 is the brand-new dividend.Step 2: Double the quotient. Have 20 in the brand-new divisor"s place.Find a number which when included to 20 and also the amount multiplied with the same number provides 28 or much less than that. 1 included to 20  is 21 and 21 × 1 = 21.Subtract 21 native 28 and get the remainder together 7. Bring down the next pair the zeros and also have 700 as the brand-new dividend.Step 3: The quotient currently is 11. Double it. We gain 22. Have actually 220 in ~ the brand-new divisor"s place.Determine a number which when added to 220 and also the sum multiplied through that number provides the product 700 or less than that. Clearly, 223 × 3 = 669.Subtract 669 native 700. Obtain the remainder 31.Now repeat the process until you approximate the quotient to 3 decimal places.

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128 lies between the 2 perfect squares √121 and √144 and hence √128 lies in between 11 and 12.Use the average an approach to approximate the evaluate √128.
The 128 in the easiest radical type is 82 and the exponential kind 128 ½ 128 = 11.313 √128 is irrational.

Example 1: Evaluate: √128 - √32

Solution:

√128 = √(64 × 2) = 8 √2√32 = √(16 × 2) = 4 √2√128 - √32 = (8 + 4 ) √2= 12 √2Therefore, √128 - √32 = 12√2


 

Example 2 : The area the a square tile is 12800 sq inches. How long is one next of this brick to the nearest tenth of one inch?

Solution: 

Area = side × side sq inches12800 = side × sideSide2 = 12800Taking the square source on both the sides, we get(side 2) ½ = (12800)½side = √128 × √100Approximating √128 come the nearest tenth, we get √128 = 11.3side = 11. 3 × 10 = 113 inches.The side of the square brick = 113 inches.


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