Square Root of 5000 + Solution With Free Steps

Square Root Of 5000

The square root of 5000 is 70.71. The nth root of a number means the number raised to the power 1/n so we can say that the square root is actually the result of a number raised to the power ½. To mathematically write the square root of a number we put the number under consideration under the √ symbol. For example, √5000= 70.71.

In this article, we will analyze and find the square root of 5000 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 5000?

The square root of the number 5000 is 70.71.

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:

√5000 = √(70.71 x 70.71)

√5000 = √(70.71)$^2$

√5000 = ±70.71

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 70.71. Hence 70.71 is 5000’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 5000?

You can calculate the square root of 5000 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 5000 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 of 5000 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 5000 using the long division method:

Step 1

First, write the given number 5000 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 5000 into pairs such as 00 and 50.

Step 3

Now divide the digit 50 by a number, giving a number either 50 or less than 50. Therefore, in this case, the remainder 1, whereas the quotient is 7.

Step 4

After this, bring down the next pair 00. Now the dividend is 100. To find the next divisor, we need to double our quotient obtained before. Doubling 7 gives 14; hence consider it as the next divisor.

Step 5

Now pair 14 with another number to make a new divisor that results in $\leq$ 100 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 0 to the divisor and multiplying 140 with 0 results in 00 $\leq$ 100. The remainder obtained is 100. Move the next pair of zeros down and repeat the same process mentioned above.

Step 7

Keep on repeating the same steps till the zero remainder is obtained or if the division process continues infinitely, solve to two decimal places.

Step 8

The resulting quotient 70.71 is the square root of 5000. Figure 1 given below shows the long division process in detail:

Square Root of 5000 by Long Division Method

Square Root by Approximation Method

The approximation method involves guessing the square root of the non-perfect square number by dividing it by the perfect square lesser or greater than that number and taking the average.

The given detailed steps must be followed to find the square root of 5000 using the approximation technique.

Step 1

Consider a perfect square number 4900 less than 5000.

Step 2

Now divide 5000 by √4900 .

5000 ÷ 70 = 71.42

Step 3

Now take the average of 70 and 71.42. The resulting number is approximately equivalent to the square root of 4900.

(70 + 71.42) ÷ 2 = 70.71

Important points

  • The number 5000 is not a perfect square.
  • The number 5000 is a rational number.
  • The number 5000 can be split into its prime factorization.

Is Square Root of 5000 a Perfect Square?

The number 5000 is not 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 5000 is concerned, it is not a perfect square. It can be proved as below:

Factorization of 5000 results in 625 x 8.

Taking the square root of the above expression gives:

= √(625 x 8)

= (625 x 8)$^{1/2}$

= 70.71

This shows that 5000 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 5000 is equivalent to 70.71.Square Root of 5000

Images/mathematical drawings are created with GeoGebra.

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