The square root of a number is the value which, when multiplied by itself, gives the original number. e.g. 10 × 10 = 100; hence, the square root of 100 is 10. Did you know that 1024 is a perfect square number? When the square root of 1024 is calculated, we will obtain an answer which is a rational number. In this lesson, we will learn to calculate the square root of 1024 by long division method. We will also go through some solved examples and interactive questions. The square root of 1024 is a number which when multiplied by itself, results in the number 1024. 1024 is an even number and a composite number. Let us determine the square root of 1024 in this article.

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**Square Root of 1024**

**:**√1024 = 32

**Square of 1024:**1024

**² =**10,48,576

1. | What Is the Square Root of 1024? |

2. | Is Square Root of 1024 Rational or Irrational? |

3. | How to Find the Square Root of 1024? |

4. | FAQs on Square Root of 1024 |

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. We know that addition has an inverse operation which is subtraction and multiplication has an inverse operation which is division. Similarly, calculating the square root of a number is the inverse operation of squaring the number. The square root of 1024 is the number which when multiplied to itself gives the number 1024. Thus, we need to think of a number whose square is 1024.**The square root of 1024 is 32.**

A rational number is a number that can be expressed in the form of p/q. A number that is not a rational number is called an irrational number. Non-terminating decimals which have repeated numbers after the decimal point are rational numbers. Now, let us look at the square root of 1024. 1024 can be broken into two factors which on multiplying give 1024. It can be written as a square of 32, which is a rational number. This shows that 1024 is a perfect square number.

Square root of 1024 is 32.The square root of 1024 is either 32 or (-32).32 and -32 can be expressed as 32/1 and -32/1. Both the numbers can be represented in the form of a rational number.Thus, the square root of 1024 is a rational number.The square root of 1024 can be calculated using different methods such as: **prime factorization and long division method**. Since 1024 is a perfect square, we can use the repetitive subtraction method as well.

### Square Root of 1024 by Prime Factorization Method

**Step 3.**Pick one factor from each pair. They can be written in the form: 2 × 2 × 2 × 2 × 2

**Step 4.**Thus, following the law of exponents, we get, √1024 = √(322) = 32 Thus, we have √1024 = +32 or -32

### Square Root of 1024 by Long Division Method

**Step 1.**Write 1024 as shown in the figure. Start grouping the number in pairs from the right. 24 is the first pair from the right and 10 is the next pair.

**Step 2**: Find the largest number that when multiplied with itself will give 10 or a number lesser than 10. Here, it is 3 (3 × 3 = 9, remainder = 1).

**Step 3**: Bring down the next pair of numbers, which is 24. The new dividend is 124. Double the quotient to get the first digit of the new divisor. The digit in the tens place will be 6.

**Step 4**: Find the digit at the units place such that when it is added to 60 and the same number is multiplied to the divisor, we get 124 or a number closest to 124.

**Step 5:**The number is 2. Now we get our new divisor as 62. 62 × 2 = 124. Complete the division and get the remainder. We finally get 0. Thus, the process of division completes here.

Therefore, **the square root of 1024 = 32**.

**Explore square roots using illustrations and interactive examples**

What is the negative root of -1024?Find the square root of 1024000 up to 5 decimal places.What is the square root of:a) 102444b) 10245

**Example 1**: The area of a square-shaped plot is 1024 square units. Calculate the measurement of one side of the plot.

**Solution:**

The area of the plot = 1024 sq. unitsTo find the side of a square-shaped plot, let us take the square root of 1024 by prime factorization method.Prime factorization of 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 21024 = (2 × 2 × 2 × 2 × 2)2√1024 = 32Therefore, the side of the square plot is 32 units.

**Example 2**: Sherin has a square blanket that has an area of 1024 square inches. The blanket has an embroidered border of a certain width. The interior area of the blanket is 400 square inches. Can you calculate the width of the embroidery of the blanket?

**Solution:**

We know that the length of each side of the blanket = √1024 = 32 inchesLength of the interior of the blanket = √400 = 20 inchesThus, width of the embroidery = 32 - 20 = 12 inches

**Example 3:** Jim is multiplying a number by itself. If the product is 1024, what is the number?

**Solution:**

To find the number, let us assume the number = qOn multiplying q times q = q × q = 1024q² = 1024q = √1024q = 32(32 × 32 = 1024)The number is 32.

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