Find the least number which must be added to 4869 to make it a perfect square

Here we will define, analyze, simplify, and calculate the square root of 4869. We start off with the definition and then answer some common questions about the square root of 4869. Then, we will show you different ways of calculating the square root of 4869 with and without a computer or calculator. We have a lot of information to share, so let's get started!
Square root of 4869 definition The square root of 4869 in mathematical form is written with the radical sign like this √4869. We call this the square root of 4869 in radical form. The square root of 4869 is a quantity (q) that when multiplied by itself will equal 4869.

√4869 = q × q = q2

Is 4869 a perfect square? 4869 is a perfect square if the square root of 4869 equals a whole number. As we have calculated further down on this page, the square root of 4869 is not a whole number. 4869 is not a perfect square.
Is the square root of 4869 rational or irrational? The square root of 4869 is a rational number if 4869 is a perfect square. It is an irrational number if it is not a perfect square. Since 4869 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 4869?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

√4869 is an irrational number

Can the square root of 4869 be simplified? You can simplify 4869 if you can make 4869 inside the radical smaller. We call this process "to simplify a surd". The square root of 4869 can be simplified.

√4869 = 3√541

How to calculate the square root of 4869 with a calculator The easiest and most boring way to calculate the square root of 4869 is to use your calculator! Simply type in 4869 followed by √x to get the answer. We did that with our calculator and got the following answer with 9 decimal numbers:

√4869 ≈ 69.778220098

How to calculate the square root of 4869 with a computer If you are using a computer that has Excel or Numbers, then you can enter SQRT(4869) in a cell to get the square root of 4869. Below is the result we got with 13 decimals. We call this the square root of 4869 in decimal form.

SQRT(4869) ≈ 69.7782200976780

What is the square root of 4869 rounded? The square root of 4869 rounded to the nearest tenth, means that you want one digit after the decimal point. The square root of 4869 rounded to the nearest hundredth, means that you want two digits after the decimal point. The square root of 4869 rounded to the nearest thousandth, means that you want three digits after the decimal point.

10th: √4869 ≈ 69.8

100th: √4869 ≈ 69.78

1000th: √4869 ≈ 69.778

What is the square root of 4869 as a fraction? Like we said above, since the square root of 4869 is an irrational number, we cannot make it into an exact fraction. However, we can make it into an approximate fraction using the square root of 4869 rounded to the nearest hundredth.

√4869

≈ 69.78/1 ≈ 6978/100

≈ 69 39/50

What is the square root of 4869 written with an exponent? All square roots can be converted to a number (base) with a fractional exponent. The square root of 4869 is no exception. Here is the rule and the answer to "the square root of 4869 converted to a base with an exponent?":

√b = b½

√4869 = 4869½

How to find the square root of 4869 by long division method Here we will show you how to calculate the square root of 4869 using the long division method with one decimal place accuracy. This is the lost art of how they calculated the square root of 4869 by hand before modern technology was invented.

Step 1)

Set up 4869 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:

Step 2) Starting with the first set: the largest perfect square less than or equal to 48 is 36, and the square root of 36 is 6. Therefore, put 6 on top and 36 at the bottom like this:

Step 3) Calculate 48 minus 36 and put the difference below. Then move down the next set of numbers.

Step 4) Double the number in green on top: 6 × 2 = 12. Then, use 12 and the bottom number to make this problem:

12? × ? ≤ 1269

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 9. Replace the question marks in the problem with 9 to get: 129 × 9 = 1161. Now, enter 9 on top, and 1161 at the bottom:

Step 5) Calculate 1269 minus 1161 and put the difference below. Then move down the next set of numbers.

6	9
48	69	00
36
12	69
11	61
1	08	00

Step 6) Double the number in green on top: 69 × 2 = 138. Then, use 138 and the bottom number to make this problem:

138? × ? ≤ 10800

The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 7. Now, enter 7 on top:

6	9	7
48	69	00
36
12	69
11	61
1	08	00

That's it! The answer is on top. The square root of 4869 with one digit decimal accuracy is 69.7. Did you notice that the last two steps repeat the previous two steps. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.
Square Root of a Number Please enter another number in the box below to get the square root of the number and other detailed information like you got for 4869 on this page.
Notes Remember that negative times negative equals positive. Thus, the square root of 4869 does not only have the positive answer that we have explained above, but also the negative counterpart.

We often refer to perfect square roots on this page. You may want to use the list of perfect squares for reference.

Square Root of 4870 Here is the next number on our list that we have equally detailed square root information about. Copyright | Privacy Policy | Disclaimer | Contact

Solution:

Given numbers are not perfect squares

First find out the square root of the number, then round it off to the next whole number. That number is the next possible perfect square root. So we add the difference between the two to get the perfect square.

(i) The square root of 525 is calculated as

It is evident that 222 < 525

The next perfect square of a whole number is

232 = 529

Hence, the number to be added to 529

= 529 - 525

= 4

The required perfect square is 525 + 4 = 529 whose root is 23

(ii) The square root of 1750 is calculated as

This shows that 412 < 1750

Next perfect square is 422 = 1764

Hence number to be added to 1750

= 1764 - 1750

= 14

The required perfect square is 1750 + 14 = 1764 whose root is 42

(iii) The square root of 252 is calculated as

This shows that 152 < 252

Next perfect square is 162 = 256

Hence number to be added to 252

= 256 - 252

= 4

The required perfect square is 252 + 4 = 256 whose root is 16

(iv) The square root of 1825 is calculated as

This shows that 422 < 1825

Next perfect square is 432 = 1849

Hence number to be added to 1825

= 432 - 1825

= 1849 - 1825

= 24

The required perfect square is 1825 + 24 = 1849 whose root is 43

(v) The square root of 6412 is calculated as

This shows that 802 < 6412

Next perfect square is 812 = 6561

Hence number to be added to 6412 is

= 6561 - 6412

= 149

The required perfect square is 6412 + 149 = 6561 whose root is 81

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.4 Question 5

Summary:

The least numbers that need to be added to the given numbers (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412 to get a perfect square are (i) 4, (ii) 14, (iii) 4, (iv) 24, and (v) 149 and the square roots are as follows 23, 42, 16, 43 and 81.

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