Phil"s father speak him the their square shed is 400 sq. Yards in area. Phil marvels what can be the size of the sides of the shed. He takes the measuring ice cream to measure up the sides. To discover the area, we have to find the square the the sides (side x side). In stimulate to uncover the next of the square once the area is given, we must find the square root. We recognize that 20 × 20 = 400. Thus, the length of the sides of the shed is 20 yards.

You are watching: What is the square root of 400

In this lesson, we will certainly calculate the square root of 400 by long division method in addition to a couple of interesting problems.

Square root of 400: 20Square the 400: 1,60,000
1.What Is the Square root of 400?
2.Is Square source of 400 rational or Irrational?
3.How to discover the Square source of 400?
4.FAQs ~ above Square root of 400

400 = a × a = 202Then a = √400 = √(20 × 20)20 × 20 = 400 or -20 × -20 = 400The second root the 400 is +20 or - 20This mirrors that 400 is a perfect square.

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A number that can be expressed together the ratio of two integers, the is, p/q where q is not equal come 0, is called a rational number. Now, let united state look in ~ the square root of 400. 

√400 = 20 = 20/1. Thus, the square source of 400 is a reasonable number.


The square source of 400 deserve to be calculate using approaches such as: prime Factorization or Long department method or repetitive Subtraction Method.

Square root of 400 by repetitive Subtraction Method

Start indigenous 400 and also keep subtracting successive odd numbers till we attain zero. The total numbers we subtract is the square root of 400.

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

Thus, beginning from 400, we have subtracted 20 times to acquire 0. Thus, the square root of 200 is 20.


Let us follow these steps to uncover the square root of 400 by long division.

Step 1: group the digits right into pairs (For digits to the left of the decimal point, pair lock from ideal to left) by placing a bar end it. Since our number is 400, let us stand for it as inside the division symbol.Step 2: discover the biggest number such that once you multiply it through itself, the product is much less than or equal to 4. We know that 2 × 2 = 4. Now, let us divide 4 by 2.Step 3: lug down the following pair the numbers, i beg your pardon is, 00. Multiply the quotient 2 by 2 and write the in the brand-new divisor"s place. Here, it is 4.Step 4: select a number in the unit"s location for the brand-new divisor such that its product with a number is much less than or equal to 0. We understand that 4 is in the ten"s place and our product has to be 0, i beg your pardon means, 40 × 0 = 0. The complete process of the long division stops here as the remainder is 0. Thus, the quotient 20 is the square source of 400.

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Explore square roots making use of illustrations and also interactive examples.


Are every square roots rational?What are numbers with integer square roots called?Can square roots be negative?
The square root of 400 in the radical kind is expressed as 400In exponent form, the square source of 400 is expressed as 4001/2The actual roots the 400 room +20 or -20.

Example 1: Mark wants to fence his square backyard. The area of his backyard is 400 square feet. What is the size of fence wire mark will need?

Solution:

To fence his backyard, note needs to know the size of each side. All the political parties of the yard are equal as it is a square backyard. Therefore, we require to identify the square source of 400. 

20 × 20 = 400

Each side will require 20 feet that fence wire. Thus, he will need 4 × 20 = 80 feet lengthy fence wire.


Example 2: James wants to acquisition a new rug for his dining room. At the store, he finds a square rug that has an area that 100 sq. Feet. a. How long is every side of the rug?b. How numerous of those rugs are necessary to sheathe an area that 400 square feet?

Solution:

Area of one rug = 100 square feet

The size of each side that the rug is area = 100

The square root of 100 is 10.

Therefore, the size of every side of the rug is 10 feet.

To cover an area the 400 square feet, he requirements 400 ÷ 100 = 4 rugs

Thus, each side of the rug is 10 feet long and also he demands 4 rugs come cover one area the 400 sq feet.


Example 3: Help Emily identify the worth of a if a2 = 400.

Solution:

The square source of 400 have the right to be established as, 400 = a × a

Using the recognized multiplication fact, 20 × 20 = 400 and -20 × -20 = 400

a = + 20 or -20


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