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 = 11.313

**Square 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

**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 = 11.315**

**√****128 ≈ 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.

**Explore Square roots using illustrations and interactive examples: **

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 8**

**√****2 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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