 # Square Root of 1521 + Solution With Free Steps

The square root of 1521, represented by the symbol √1521, equals 39. The power 1/2 is represented by the square root symbol , which is. It means that when a number’s square root is calculated, the outcome is a number that has half the power of the original number. For instance, 196’s square root is equal to 14, or √196.

In this article, we will analyze and find the square root of 1521 using various mathematical techniques, such as the approximation method and the long division method.

## What Is the Square Root Of 1521?

The square root of the number 1521 is 39.

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:

√1521 = √(39 x 39)

√1521 = √(39)$^2$

√1521 = ±39

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 39. Hence 39 is 1521’s square root. The square root generates both positive and negative integers.

## How To Calculate the Square Root of 1521?

You can calculate the square root of 1521 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 1521 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 1521 using the long division method:

### Step 1

First, write the given number 1521 in the division symbol, as shown in figure 1.

### Step 2

Starting from the right side of the number, divide the number 1521 into pairs such as 21 and 15.

### Step 3

Now divide the digit 15  by a number, giving a number either 3 or less than 3. Therefore, in this case, the remainder is 6  whereas the quotient is 3.

### Step 4

After this, bring down the next pair 21. Now the dividend is 621. 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 2 with another number to make a new divisor that results in $\leq$ 621 when multiplied with the divisor. If the number is not a perfect square, add pair of zeros to the right of the number before starting division.

### Step 6

Adding 9 to the divisor and multiplying 69 with 9 results in 621 = 621. The remainder obtained is 0.

### Step 7

The resulting quotient 39 is the square root of 1521. Figure 1 given below shows the long division process in detail: Figure 1

### Important points

• The number 1521 is a perfect square.
• The number 1521 is a rational number.
• The number 1521 can be split into its prime factorization.

## Is Square Root of 1521 a Perfect Square?

The number 1521 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 1521 is concerned, it is a perfect square. It can be proved as below:

Factorization of 1521 results in 39 x 39 which can also be expressed as 39$^2$.

Taking the square root of the above expression gives:

= √(39$^2$)

= (39$^2$)$^{1/2}$

= 39

This shows that 1521 is a perfect square and a rational number.

This shows that 1521 is not a perfect square as it has decimal places; hence it is an irrational number.

Therefore the above discussion proves that the square root of 1521 is equivalent to 39.

Images/mathematical drawings are created with GeoGebra.

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