Square root of 50 – Calculation, derivation and examples

Value of root 50

We know that root is the inverse of power. Five raised to the power of 2, is 25; and 25 is the square of 5. It means that the square root of 25 is 5. Now, if we look at 50, we’ll get to know that it isn’t a perfect square i.e.; its square root is not a whole number. Therefore, 50 is an imperfect square.

The square root of 50 is an irrational number owing to the fact that 50 isn’t a perfect square. It can have an infinite number of decimals and they won’t terminate, thereby making it difficult to turn it into an exact fraction.

How to find the value of √50

Method-1:Determining value of root 50 by Long Division method

Step 1: We start by placing a bar over the digits 50. Now, pair the zeros in decimals from left to right.

Step 2: Now, we’ll find a number such that when we multiply it by itself, will yield a product that is less than or equal to 50. We know that the square of 7 is 49 which is less than 50. Dividing 50 by 7 gives 7 as the quotient and 1 as the remainder.

Step 3: Next, we’ll place a decimal after the quotient as we are now dividing using the 0s from the decimal part of 50. Now, 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 14c as our new divisor. ‘c’ being an unknown digit. We need to find a value of c such that 14c × c gives us a value that is less than 100. The only digit that fills c position, giving us a resultant value of less than 100 is 0, we place it after ’14’ and therefore the dividend becomes 140 and the quotient is now 7.0

Step 5: The next divisor will be 1400 and the dividend will be 10000.

The same process will be continued until we get the answer nearest to the desired decimals.

Method-2:Determining the value of root 50 by Prime Factorisation method

This method involves the factorisation of the number and pulling the roots of any perfect squares that one may find out of the radical sign.

Step 1: Simplify the number given by breaking it down into its factors. It is essential to factorise the number until you’ve achieved all prime numbers.

Step 2: Combine the factors using exponents. For example, 5×5 can also be written as 5².

Step 3: Move the bases outside the radical sign.

Step 4: If you’re left with any value inside the radical sign, determine its roots by using the Division Method. Multiplying the value outside the radical sign with the root of value inside it gives us the desired value.

Solved Question

Q1) Determine ‘x’ if x² = 200
If x² = 200
x = √200
x = √ (50 x 4)
x = √ (50 x 2 x 2)  = 2√50
x = 2 x 7.0710
x = 14.1420

Q2) The area of a square park is 50m². Find the length of each side of the park.
Given,
Area or square park = 50m² We know, area of square = a² (where a= side of square)
a² = 50m²
Therefore, each side of the park (a) = √50 m² Each side of the square park is 7.071 m long.