In Maths, the square source of 24 is same to 2√6 in radical type and 4.898979485 in decimal form. The product the the square root of a number through itself, produce the original number. Therefore, square source is the reverse procedure of squaring a number. If √24 = x, climate x2 = 24. Hence, square source generates the root value of the original number.

You are watching: Whats the square root of 24

The square root of 24 is denoted by √24, where ‘√’ is the radical symbol and also the number under the root is the radicand. Since, √2 is an irrational number, therefore, √24 = 2√6 is also an irrational number.

Square root of 24 = √24 = ±2√6

Or

In decimal form,

√24 = 4.898979485

Or

In Exponent Form,

(24)½ = 4.898979485

24 is not a perfect square, it means the square of no organic number generates the worth equal come 24. Therefore, the square source of 24 will not be a whole number. Currently to find the exact value that √24 we have the right to use the long division method. Although the simplest form of √24 can be evaluated utilizing the element factorisation method.

Also check:

How to find the Square root of 24?

There are two basic methods, we deserve to use to uncover the square source of 24:

Prime Factorisation Method

By the prime factorisation method, we have the right to write:

24 = 2 × 2 × 2 × 3

Or we can write the over expression as:

24 = (2 x 2) x 2 x 3

24 = 22 x 2 x 3 Now, acquisition square source on both the sides, we get;

sqrt24 = sqrt2^2 imes 2 imes 3

Taking the end the square term the end of the root, us get;

√24 = 2√6

This is the simplest kind of square source of 24.

We can more put the worth of √6 and simplify.

Since, the value of √6 = 2.5 (approx)

Therefore, √24 = 2√6 = 2 x 2.5 ≈ 4.9

Facts:Square source of 24 is one irrational number 24 is an even composite number24 is an imperfect square, the worth of √24 is no a natural numberThe root of 24 room +2√6 or -2√6

Long department Method

Long division method is supplied to find the square root of any number through accuracy. This is additionally a shortcut technique to uncover the square source of 24. One can quickly learn this an approach and apply, after analysis the listed below given steps.

Step 1: create the number 24 as 24.00 00 00 00Step 2: Now, we have actually to group the digits in a pair the two and also place a bar over each pairStep 3: take a number that deserve to be multiply by itself, such the the result is much less than or same to 24. Thus, 4 x 4 = 16Step 4: Subtract 16 from 24 to acquire 8 and include 4 to the previous divisor to get 8. Take under the 2 zeros and also write next to 8 top top the dividend side.Step 5: Again take a number and also put in ~ the unit place of divisor together that when the new divisor is multiplied by the number, it is much less than or same to 800. Thus, 88 x 8 = 704Step 6: Repeat the above two actions again and get the quotient upto two locations of decimals.Therefore, the result is 4.89 as presented in the below diagram

*

Students deserve to repeat the steps to acquire the square root value up to four decimal places.

Approximation Method

This technique can additionally be offered to discover the square source of one imperfect square. It will certainly generate one approximate worth which is an extremely close to the actual value of a square root. For one or 2 digit numbers, we can use this method to uncover the square source of it. Since, we know the square root of perfect numbers from 1 to 10 as provided below:

11
24
39
416
525
636
749
864
981
10100

Now, we need to see where the number 24 lies between the squared terms.

Clearly, that lies in between 16 and 25, hence between 42 and also 52.

Thus, we can conclude 24 is the square of a number less than 52. Hence, the first digit of √24 is 4.

Now, we have to find the digits after decimal.

Decimal component = (Actual number- lower perfect square) /(Higher perfect square-Lower perfect square)

= (24-16)/(25-16)

= 8/9

= 0.88888…

Therefore, the worth of √24 = 4.888888…

Or √24 = 4.89

Hence, us have gained the correct answer.

Repeated individually Method

Repeated individually is additionally a method of recognize the square root. But it is applicable just for perfect squares. Because 24 is a non perfect square number, as such we cannot use the method to discover it’s square root.

In repetitive subtraction, we subtract continuous odd numbers beginning from the original number till we get last value same to zero. The total variety of times, the subtraction is done, will tell us the square root value. If we shot this technique to find the square source of 24 then;

24 – 1 = 2323 – 3 = 2020 – 5 = 1515 – 7 = 88 – 9 = -1

Since, we have got negative integers together a an outcome of subtraction but not zero, therefore we cannot find the square source of 24 here.

Square root of Numbers

√204.472
√214.583
√224.690
√234.796
√244.899
√255.000
√265.099
√275.196
√285.292
√295.385

Solved Examples

Q.1: uncover the value of 7 multiplied by √24.

Solution: 7 multiply by √24 is:

7 x √24

Since, the worth of √24 = 4.89

Therefore,

7 x √24

= 7 x 4.89

= 34.23

Q.2: discover the size of a chessboard whose area is equal to 24 sq.cm.

Solution: Given, area that chessboard = 24 sq.cm.

Since, the chessboard is in square shape. Therefore,

Area of the chessboard = (side)2

Side = (Area)1/2

Side = √24

Side = 2√6 cm.

Hence, the size of the side of the chessboard is 2√6 sq.cm.

Q.3: What is the worth of (√24)3?

Solution: The value of (√24)3 is:

(√24)3 = (2√6)3

= 23 x (√6)3

= 8 x 6√6

= 48√6

Q.4: What is five times that the square root of 24?

Solution: five times that square root of 24 = 5 x √24

⇒ 5 x 4.89

⇒ 24.49

Therefore, five times the square source of 24 is 24.49.

See more: 60+ Food That Starts With An E, 42 Foods That Start With E

Practice Questions

√24 + √6 – 2√6 = ?How to create the square root of 24 in radical form?What is a perfect square simply next to number 24?What is the additive inverse of √24?What is the multiplicative inverse of √24?

Register with us and also download BYJU’S – The Learning application to learn an ext about squares and square roots v the assist of interactive videos.