Square Root Of 400 Simplified

Foursquare root of 400 is a value that tin can exist squared to get the original number. Suppose x is the root of 400, then xⁱⁱ = 400. Basically, a square root is the inverse process of squaring a number. Since, 400 is a perfect square, therefore it is easy to find the square root value.

The square root of 400 is represented by √400, where '√' is the radical symbol and the value under the root is the radicand. √400 is twenty, which is a rational number. To find the square root, nosotros can use the simple prime factorisation method or long partition method.

Square root of 400 = √400 = ±20

In Exponent Form,

(400)^½ = ±20

Also check:

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How to Discover the Square root of 400?

Square root of 400 is a rational number that can be represented in the form of a numerator and denominator.

At that place are three methods to find the square root of 400, they are:

Prime Factorisation Method
Partitioning Method
Repeated Subtraction Method

Prime Factorisation Method

This method is mostly recommended when we need to discover the square root of perfect squares. In this method, we find the prime factors form of 400 and so take the square root on both the sides.

The prime factorisation of 400 is:

400 = 2 10 two x 2 ten 2 10 5 x 5

If we write in exponential class, then;

400 = 2⁴ ten 5²

400 = 2² x 2² 10 v² [Using laws of exponents]

Taking foursquare root on both sides of the equation, we get;

\(\begin{array}{50}\sqrt{400} = \sqrt{two^{2}\times 2^{2}\times 5^{2}}\end{assortment} \)

If we dissever the roots for each term, then;

\(\begin{array}{l}\sqrt{400} = \sqrt{2^{2}}\times \sqrt{2^{2}}\times \sqrt{5^{2}}\finish{array} \)

Now, nosotros can abolish each of the square root on the right paw side of the equation, with the square of each term. Therefore, we get;

√400 = 2 ten 2 ten 5

√400 = 20

Hence, nosotros got the square root of the rational number 400, which is as well a rational number.

Facts:

Square root of 400 is a natural or a whole number
400 is an even number and and then is information technology'due south foursquare root
400 is evenly divisible by its square root value, thus, 20 is the gene of 400.
The roots of 400 are +twenty or -20.
400 sq.units is the area of a square that has side length equal to 20 units.

Long Division Method

Finding the square root of a number, using long partitioning, is the fastest method. This method is most efficient when we find the square root of imperfect squares because it is difficult to find the square root of imperfect numbers using prime factorisation. Square root of imperfect numbers results in decimal value. Long segmentation method is also useful to observe the root of big numbers.

Permit us find here the square root of 400 using a long segmentation method.

Step ane: Group the digits of the original number in pairs from right to left and put the bar over each pair. Thus, iv and 00 are two groups hither.

Step 2: Now we volition begin with divisions. Take the greatest number, which can be multiplied by itself to get a value equal to iv, such that 4 gets subtracted from 4. Hence, we get 0.

Stride 3: Write the next pair of numbers, i.due east., 00, on the dividend side and add 2 on the left side, such that 2 + 2 = iv is the new divisor.

Footstep four: At present nosotros need to attach iv (on the left side) with such a number such that when multiplying the divisor with the same number, the resulting values cancel the consummate dividend. Hence, xl multiplied by 0 results in 00.

The whole division process is given beneath:

Square root of 400

Therefore, the square root of 400 is equal to twenty, as per the long partition method.

Repeated Subtraction Method

This method is also applicable merely for perfect squares. In this method, we start subtracting the original number past the set of odd numbers, in a successive manner, such that at the end we get zero. The number of times we subtract with the odd numbers is equal to the required foursquare root. For instance, if we subtract the number 5 times so the foursquare root of the number is 5. Let usa see how it works.

400 – ane = 399
399 – 3 = 396
396 – 5 = 391
391 – 7 = 384
384 – ix = 375
375 – eleven = 364
364 – 13 = 351
351 – fifteen = 336
336 – 17 = 319
319 -19 = 300
300 – 21 = 279
279 – 23 = 256
256 – 25 = 231
231 – 27 = 204
204 – 29 = 175
175 – 31 =144
144 – 33 =111
111 – 35 = 76
76 – 37 = 39
39 – 39 = 0

Therefore, we can see, the subtraction method is done for xx times. Only later the 20th time, we got the departure equal to zero. Therefore, the square root of 400 is 20.

Square Roots of Perfect Numbers

Square Root of 25 = 5
Square root of 49 = 7
Square root of 81 = 9
Foursquare root of 100 = 10
Square root of 169 = 13
Square root of 225 = 15
Square root of 289 = 17

Video Lessons on Square Roots

Visualising square roots

Finding Foursquare roots

Solved Examples

Q.1: What is the value of ten multiplied past √400?

Solution: The value of 10 multiplied by √400 is:

⇒ ten x √400

⇒ 10 x 20

⇒ 200

Hence, the answer is 200.

Q.ii: If the area of a square shaped field is 400 m², what is the value of its length and latitude?

Solution: Given that,

Expanse of the field = 400 m²

Area of the square = Side²

Since the field is in square shape, therefore the length and breadth of the field will be equal. Therefore,

Expanse of the field = Length²

400 = Length²

Length = √400 = 20

Hence, the value of length and breadth of the field is xx meter, respectively.

Q.3: If the area of square is 400 units, then find the perimeter of the square.

Solution: Given,

Area of the square = 400 units

Therefore,

Side of the foursquare = √area = √400 = 20 unit

Therefore, the perimeter of the square is;

Perimeter = 4side = 4 10 xx = 80 units.

Practice Questions

√400 + √100 + √25 = ?
You accept a square blanket of 400 sq.inches. What is the length of ane side of the blanket?
A foursquare table has 20 cm of length. What is the area of the table?
The surface area of the room is 400 square feet. What is the perimeter of the room?

Annals with us and download BYJU'Due south – The Learning App to larn more well-nigh squares and square roots with the assistance of interactive videos.

Frequently Asked Questions on Square root of 400

What is the square root of 400?

The square root of 400 is equal to 20.
√400 = 20

Is the square root of 400 rational or irrational?

The square root of 400 is a rational number considering it tin can be represented in the grade of a ratio or p/q.
√400 = xx = xx/ane
Where xx is the numerator and i is the denominator.

Is 400 a perfect square?

Yep, 400 is a perfect square because the square of the real number 20, results in the actual number.
xxⁱⁱ = 400

Which is the fastest method to find the square root of 400?

Since 400 is a perfect foursquare and only a 3 digit number, therefore we can use a long division method to find the foursquare root, quickly.

What is the value of the square root of 4000?

The foursquare root of 4000 is an irrational number, since it is not a perfect square.
√4000 = xx√10
If we further simplify the in a higher place value, we volition get the decimal value which is non-terminating and non-repeating.
√4000 = 63.2455532033676