Square Root of 59

The Square Root 59 is a number which when multiplied by itself, results in the number 59. 59 is also a prime number which makes it trickier to calculate its square root. We will learn how to calculate the Square Root of 59 and look at a few problems to help us understand this topic.

Square Root of 59: √59= 7.6811457...
Square of 59: 59² = 3481

The square root of a number is a number which when multiplied by itself, results in the original number. For example, the square root of 25 is 5, as 5 times 5 results in 25 which makes it a perfect square. However, you can also have square roots of some numbers that do not result in whole numbers, such as 59. We can express the square root of 59 in different ways

• Decimal form: 7.681
• Radical form: √59
• Exponent form: (59)^1/2

• 59 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
• Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 59 is an irrational number.

Since we concluded that the square root of 59 is non-terminating, we can only use 2 methods to calculate the value of its square root

• Long Division Method
• Estimation and Approximation Method

Long Division

• Step 1: Starting from the right, we will pair up the digits 59 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
• Step 2: Think of a number whose square is less than or equal to 59. In this case, that number would be 7.
• Step 3: Dividing by 59 by 7 with quotient set as 7, we get a remainder of 10. 
• Step 4: Drag a pair of 0’s down and fill it next to the remainder to make it 1000. 
• Step 5: The divisor, in this case 7 is doubled and written below. Now, we have 14X as the new divisor, and we need to find a value of X that makes the product of 14X × X less than or equal to 1000. In this case, 146 is the required value
• Step 6: The number 6 is placed in the quotient after a decimal place. The new divisor for the next division will be 146 + 6 = 152.
  Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.

Therefore, the square root of 59 = 7.681

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

• Step 1: Find a perfect square that is smaller than and bigger than 59. In this case, 7 and 8 will work as their squares are 49 and 64.
• Step 2: Writing in terms of inequality- 7<√59<8 = 49<59<64
• Step 3: Multiply by 100 and write in terms of square roots- √4900<√5900<√6400
• Step 4: Move closer to inequality- √5776<√5900<√5929 = 76<10√59<77
  = 7.6<√59<7.7
• Step 5: Taking average of upper and lower limits we get, (7.6 + 7.7)/2 = 7.65

Therefore, we can estimate the square root of 59 ≅ 7.65

Explore Square roots using illustrations and interactive examples

• Square Root of 60
• Square Root of 61
• Square Root of 50
• Square Root of 58
• Square Root of 49

• What is the square root of 59 up to 6 decimal places(Use Long Division)
• What are the roots of -59? Also, find the value of the square of the negative root of -59

What is the square root of 59?

The square root of 59 is √59= 7.681.

Is the square root of 59 a rational number?

No, the square root of 59 is not a rational number since the square root of 59 is non-terminating and cannot be represented in the form of p/q.

What is the square root of 59 in the simplest radical form?

√59 is the simplest radical form.

What is the square of 59?

The square of 59 is 59² = 3481

Can we find the square root of 59 by the prime factorization method?

No, we can’t find the square root of 59 by the prime factorization method. This is because it is a prime number and its only factors are itself and 1. Therefore we cannot simplify it further.