# What Is The Square Root Of 256, How To Find The Square Root Of 256

The number 256 is significant in our everyday lives. It is the number of colors in a GIF or a bitmap. It is also the number of regular football games in an NFL season.Mathematically, it is a perfect square.In this mini-lesson, we will learn about the square root of 256 simplified, the square root of 256 by division method, and the square root of 256 by prime factorization.

Đang xem: What is the square root of 256

Square Root of 256: 16Square of 256: 65,536

 1 What Is the Square Root of 256? 2 Is Square Root of 256 Rational or Irrational? 3 How to Find the Square Root of 256? 4 FAQs on Square Root of 256

The square root of a number is the number which, whenmultiplied to itself, gives the original number.For any two real numbers, a and b, a2= b anda = √b.Let us understand the calculation of the square root of 256.The square root of 256 is the number which, when multiplied with itself, willgive the result as 256.The square root of 256 is the inverse operation of squaring 16.If 162 =256, then √256 = 16

When we multiplytwo negative signs, we get a positive sign.The multiplication of (-16)with itself will give the result as 256. Therefore, (-16) is also a square root of 256.We will study the mathematical approach to calculatethe square root of 256 in the following sections.
The square root of 256 is either 16 or (-16).13 and -13 can be expressed as 16/1 and -16/1.Both the numbers can be represented in the form of a rational number.Thus, the square root of 256 is a rational number.

The square root of 256 can be calculatedusing different methods such as:Prime Factorization and Long Division method.

### Square Root of 256 by Prime factorization method

Step 3.Pick one factor from each pair and they can be written in the form: 256 = (2 × 2 × 2 × 2)2Step 4. Thus, following the law of exponents, we get,√256 =√(162) = 16½Thus we evaluate √256 = + 16 or -16
Step 1. Write 256 as shown in the figure. Start grouping the number in pairs from the right end. 56 is the first pair from the right.

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Step 2: Find the largest number that when multiplied with itself will give 2or a smallernumber closest to 2. Here it is 1.Do the division and get the remainder.Step 3: Bring down the next pair of numbers. Here it is 56.Multiply the quotient 1 by 2 and write it in the new divisor's place or the tens place. The number2 will be placed in the tens place.Step 4:Find the largest number that when kept at ones place with 2 at tens place multipliedwith that same number gives a result 156or anumber closest to 156.Step 5:Get the next quotient place as 6. Now we get our new divisor as 26 as6 ×26= 156.Complete the division and get the remainder.Here we get 0.Thus, the process of division completeshere.

Explore square roots using illustrations and interactive examples.

Roger was planning to cover a squaretable that has an area of √256 square inches. He found a clothof area 18square inches.How many inchesdoes the cloth hang over the table on each side if the cloth iscentered on the table?
The square root of 256is expressed as √256in the radical form and as 256½ in the exponential form.

Example 1:Chrisorders a pizza whose surface area is 803.84square inches. What is the radius of the pizzathat Chris ordered?

Solution:

The total surface area of Chris's pizza= 803.84 square inches

The surface area of a circle =π ×r2

3.141 ×r2 = 803.84

r2= 803.84÷3.141 = 256

r = √256

r =+16 or -16

Since the radius cannot be negative, we need toconsider the positive value.

Therefore, the radius of the pizzathat Chrisordered = 16inches.

Example 2: Veronica makes as many bracelets in a dayas the number of days that she has taken to make 256 of them. If she has made a total of 256 bracelets, how many bracelets has she made and how many days has she taken?

Solution:

Number of bracelets made = number of days taken.

Let the number of bracelets made per day = n

Let the number of days taken = n

n× n = 256

n2 = 256

n = 16

Thus, she has taken 16 days to make 16 bracelets per day.

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