# what is the square root of 256

Video The square root of 256 The square root of 256 The square root of 256 is expressed as √256 in root and as (256) ½ or (256) 0.5 in power. The square root of 256 is 16. It is a positive solution of the equation x2 = 256. The number 256 is a perfect square.

• Square root of 256: 16
• Square root of 256 in exponential form: (256) or (25) 0.5
• Square root of 256 in root form: 256

1. What is the square root of 256? 2. Is the square root of 256 Reasonable or Unreasonable? 3. How to Find the Square Root of 256? 4. FAQ about Square Root of 256

• The square root of a number is the number that, when multiplied by itself, gives the original number.
• For any two real numbers a and b, a2 = b and a = √b.
• Let us understand the calculation of the square root of 256.
• The square root of 256 is a number that, when multiplied by itself, gives 256.
• The square root of 256 is the inverse of the square of 16.
• If 162 = 256 then 256 = 16

Read: What is the square root of 256

• When we multiply two negative signs, we get one positive sign.
• Multiplying (-16) by itself gives 256. Therefore, (-16) is also a square root of 256.
• We will study the mathematical approach to calculating the square root of 256 in the following sections.
• A rational number is defined as a number that can be expressed as a quotient or a division of two integers, i.e. p/q where q is not zero.
• The square root of 256 is 16 or (-16).
• 13 and -13 can be represented as 16/1 and -16/1.
• Both numbers can be represented as a rational number.
• Therefore, the square root of 256 is a rational number.

The square root of 256 can be calculated using different methods such as: Prime factorization method and long division method.

### Square root of 256 by prime factorization method

• Step 1: Determine prime factors using prime factors. Prime factor of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2
• Step 2. Group the prime factors obtained for 256 into pairs.
• Step 3. Choose a factor from each pair and they can be written as: 256 = (2 × 2 × 2 × 2) 2
• Step 4. Thus, obeying the law of exponents, we get, 256 = (162) = 16½
• Therefore, we evaluate √256 = +16 or -16
• Step 1. Write 256 as shown in the picture. Start grouping numbers in pairs from the bottom right. 56 is the first pair from the right.
• Step 2: Find the largest number that, when multiplied by itself, gives 2 or the smaller number closest to 2. This is 1. Do the division and get the remainder.
• Step 3: Lower the next pair of numbers. This is 56. Multiply the quotient 1 by 2 and write that quotient in the new divisor or tens place. Number 2 will be placed in the tens.
• Step 4: Find the largest number that, when kept in the units row with 2 in the tens, multiplied by the same number gives 156 or the closest number to 156.
• Step 5: Take the next quotient as 6. Now we get a new divisor of 26 which is 6 × 26 = 156. Complete the division and get the remainder. Here we get 0. Thus, the division is complete here.

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• The square root of 256 is expressed as √256 in root and 256½ in exponential form.