Square source of 400 is a worth that have the right to be squared to obtain the original number. Suppose x is the root of 400, climate x2 = 400. Basically, a square source is the inverse process of squaring a number. Since, 400 is a perfect square, therefore it is basic to uncover the square source value.

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The square source of 400 is represented by √400, wherein ‘√’ is the radical symbol and also the value under the source is the radicand. √400 is 20, which is a reasonable number. To find the square root, we deserve to use the straightforward prime factorisation an approach or long department method.

Square root of 400 = √400 = ±20


In Exponent Form,

(400)½ = ±20

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How to discover the Square source of 400?

Square source of 400 is a reasonable number that deserve to be represented in the type of a numerator and denominator.

There room three approaches to find the square source of 400, castle are:

Prime Factorisation Method

This an approach is largely recommended once we need to discover the square root of perfect squares. In this method, we uncover the prime factors form of 400 and then take the square root on both the sides.

The element factorisation that 400 is:

400 = 2 x 2 x 2 x 2 x 5 x 5

If we compose in exponential form, then;

400 = 24 x 52


400 = 22 x 22 x 52 Taking square root on both sides of the equation, us get;

(sqrt400 = sqrt2^2 imes 2^2 imes 5^2)

If we different the roots because that each term, then;

(sqrt400 = sqrt2^2 imes sqrt2^2 imes sqrt5^2)

Now, we have the right to cancel each of the square root on the ideal hand side of the equation, through the square of every term. Therefore, we get;

√400 = 2 x 2 x 5

√400 = 20

Hence, we obtained the square source of the rational number 400, i m sorry is additionally a rational number.


Square source of 400 is a organic or a totality number400 is an even number and also so is that square root400 is evenly divisible by its square root value, thus, 20 is the factor of 400.The root of 400 are +20 or -20. 400 sq.units is the area that a square that has side size equal to 20 units.

Long division Method

Finding the square source of a number, using long division, is the more quickly method. This an approach is most efficient when we uncover the square source of imperfect squares due to the fact that it is an overwhelming to uncover the square source of imperfect numbers using prime factorisation. Square source of imperfect numbers results in decimal value. Long department method is also useful to discover the source of huge numbers.

Let us uncover here the square root of 400 making use of a long division method.

Step 1: team the digits of the original number in bag from appropriate to left and also put the bar over each pair. Thus, 4 and also 00 room two groups here.

Step 2: now we will start with divisions. Take it the biggest number, which can be multiplied by itself to get a worth equal come 4, such that 4 it s okay subtracted indigenous 4. Hence, we get 0.

Step 3: compose the next pair that numbers, i.e., 00, on the dividend side and add 2 on the left side, such that 2 + 2 = 4 is the brand-new divisor.

Step 4: currently we need to affix 4 (on the left side) v such a number together that as soon as multiplying the divisor through the exact same number, the resulting values cancel the complete dividend. Hence, 40 multiply by 0 results in 00.

The whole department process is given below:


Therefore, the square source of 400 is equal to 20, as per the long division method.

Repeated subtraction Method

This method is additionally applicable just for perfect squares. In this method, we start subtracting the initial number by the set of odd numbers, in a successive manner, such the at the finish we obtain zero. The variety of times us subtract with the odd number is same to the forced square root. Because that example, if us subtract the number 5 times climate the square source of the number is 5. Let united state see how it works.

400 – 1 = 399399 – 3 = 396396 – 5 = 391391 – 7 = 384384 – 9 = 375375 – 11 = 364364 – 13 = 351351 – 15 = 336336 – 17 = 319319 -19 = 300300 – 21 = 279279 – 23 = 256256 – 25 = 231231 – 27 = 204204 – 29 = 175175 – 31 =144144 – 33 =111111 – 35 = 7676 – 37 = 3939 – 39 = 0

Therefore, we deserve to see, the subtraction technique is done for 20 times. Only after the 20th time, we acquired the distinction equal come zero. Therefore, the square root of 400 is 20.

Square roots of Perfect Numbers

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

Solved Examples

Q.1: What is the value of 10 multiply by √400?

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

⇒ 10 x √400

⇒ 10 x 20

⇒ 200

Hence, the answer is 200.

Q.2: If the area that a square shaped field is 400 m2, what is the value of that length and breadth?

Solution: offered that,

Area that the ar = 400 m2

Area of the square = Side2

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

Area the the field = Length2

400 = Length2


Length = √400 = 20

Hence, the worth of length and breadth that the ar is 20 meter, respectively.

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

Solution: Given,

Area the the square = 400 units


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

Therefore, the perimeter that the square is;

Perimeter = 4side = 4 x 20 = 80 units.

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Practice Questions

√400 + √100 + √25 = ?You have a square blanket of 400 sq.inches. What is the length of one side of the blanket?A square table has actually 20 cm of length. What is the area the the table?The area the the room is 400 square feet. What is the perimeter that the room?

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