Square Root of 50

The square root of 50 is a number which when multiplied by itself results in 50. Finding the square root of a number is extremely important for finding the side length of a square from its area. We will now look at how to find the value of the square root of 50 and solve some problems to help give you a better understanding.

• Square Root of 50: √50 = 7.0710678...
• Square of 50: 50² = 2500

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. However, you can also have square roots of some numbers that do not result in whole numbers, such as 50. We can express the square root of 50 in different ways:

• Decimal form: 7.071
• Radical form: √50 = 5√2
• Exponent form: 50^1/2

• The decimal part of the square root 50 is non-terminating. This is the definition of an irrational number. It also cannot be expressed as a ratio p/q which tells us it is irrational.
• Looking at the decimal form of the root 50, we see that it is never ending: √50 = 7.0710678118…….
• Therefore, we can conclude that Square Root of 50 is Irrational.

There are 2 main methods we use to find the Square Root of 50:

• Prime Factorization
• Long division

Prime Factorization

• To find the square root of 50, we shall first express it in terms of its prime factors.

50 = 2 × 5 × 5 

• Next, this can be reduced further to  50 = 2 × 5²
• Finally, to find the root of this from here it is very easy, 

√50 = √(25 × 2) = 5√2 = 5 × 1.414 = 7.07

Therefore, the Square Root of 50 ≅ 7.07

Long Division

• Step 1: Place a bar over the digits 50. We also pair the 0s in decimals in pairs of 2 from left to right.
• Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 50. We know that 7 × 7 = 49 which is less than 50. Dividing 50 by 7 we get 7 as quotient and 1 as remainder.
• Step 3: Place a decimal after the quotient as we are now dividing using the 0s from the decimal part of 50. Remember to drag down the pair of 0s, making the dividend 100. Also, adding 7 by itself gives us 14 which becomes the starting digits of our next divisor.
• Step 4: Now we have 14X as our new divisor. We need to find a value of X such that 14X × X gives us a value less than 100. Only 0 fills X position and therefore the dividend is 140 and quotient is now 7.0.
• Step 5: The next divisor will be 140 + 0 and dividend will be 10000. We continue doing the same steps till we get the number of decimals we require.

So our long division now looks like this: 

Therefore, the Square Root of 50 is 7.071

Explore Square roots using illustrations and interactive examples

• Square Root of 100
• Square Root of 10
• Square Root of 25
• Square Root of 5
• Square Root of 15

• What is the square root of 450?
• Is -7.071 a root of 50? If yes, why?
• Find the square root of: 
  • 0.5
  • 500000

What is the square root of 50?

The square root of 50 is √50 = 7.071.

What is the square of 50?

The square of 50 is 50² = 2500.

What is the square root of 50 simplified?

The square root of 50 in simplified form is 5√2.

Is the square root of 50 a rational number?

The square root of 50 is an irrational number as it is non-terminating. It cannot be expressed in the form p/q which is what makes a rational number.

What is the exponent form of root 50?

The exponent form if root 50 is 50^1/2.