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Square Root of 1024 + Solution With Free Steps

The square root of 1024 which can mathematically be written as √1024 is 32.  1024 is a perfect square so its square root is a rational number. A perfect square is a number that is the square of an integer.  When we multiply an integer by itself the result is a perfect square.

 

In this article, we will analyze and find the square root of 1024 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 1024?

The square root of the number 1024 is 32.

The square root can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:

√1024 = √(32 x 32)

√1024 = √(32)$^2$

√1024 = ±32

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 32. Hence 32 is 1024’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 1024?

You can calculate the square root of 1024 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.

The symbol √ is interpreted as 1024 raised to the power 1/2. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.

Let us discuss each of them to understand the concepts better.

Square Root by Long Division Method

The process of long division is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.

Learning how to find the square root of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.

Following are the simple steps that must be followed to find the square root of 1024 using the long division method:

Step 1

First, write the given number 1024 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 1024 into pairs such as 24 and 10.

Step 3

Now divide the digit 10 by a number, giving a number either 10 or less than 10. Therefore, in this case, the remainder is 1, whereas the quotient 3.

Step 4

After this, bring down the next pair 24. Now the dividend is 124. To find the next divisor, we need to double our quotient obtained before. Doubling 3 gives 6; hence consider it as the next divisor.

Step 5

Now pair 6 with another number to make a new divisor that results in $\leq$ 124 when multiplied with the divisor. 

Step 6

Adding 2 to the divisor and multiplying 62 with 2 results in 124 $\leq$ 124. The remainder obtained is 0. 

Step 7

The resulting quotient 32 is the square root of 1024. Figure 1 given below shows the long division process in detail:

Square root of

Figure 1

Important points

  • The number 1024 is a perfect square.
  • The number 1024 is a rational number.
  • The number 1024 can be split into its prime factorization.

Is Square Root of 1024 a Perfect Square?

The number 1024 is a perfect square. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.

A number expressed in p/q form is called a rational number. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.

A number that is not a perfect square is irrational as it is a decimal number. As far as 1024 is concerned, it is a perfect square. It can be proved as below:

Factorization of 1024 results in 32 x 32 that can also be expressed as 32$^2$.

Taking the square root of the above expression gives:

= √(32$^2$)

= (32$^2$)$^{1/2}$

= 32

This shows that 1024 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of X is equivalent to y.

Images/mathematical drawings are created with GeoGebra.

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