Square Root of 50

The square root of 50 (√50) is a value that can be multiplied by itself to get the original number. The value of the square root of 50 is equal to 5√2 in radical form and 7.0710678.., in decimal form. As we can see, the root of 50 is not a whole number but a decimal or a fraction. Hence, 50 is not a perfect square. To find the square root of 50, we have to use the long division method.

What is the Square Root of 50?

According to the definition, the square root of any number is the value that is squared or multiplied by itself to get the original number. Thus, the square root is the opposite process of squaring a number. Thus, the square root of 50 is the value that is squared to get the original number. The simplified form of the square root of 50 is 5√2 or 7.07 (approximately).

Square root of 50 can be represented in three forms.

The square root of 50, 7.0710678…, is an irrational number since it is a non-terminating decimal. Thus, we cannot represent root 50 in the form of P/Q. Representing root 50 in a number line is quite challenging as compared to whole numbers.

How to Find the Square Root of 50?

To find the square root of 50, we have two methods here:

• Prime Factorisation
• Long Division Method

Let us learn both the methods, one by one.

Prime Factorisation

50 is a composite number, thus we can find its prime factorisation by dividing it by prime numbers.

• 50 is represented as the product of prime factors

50 = 2 x 5 x 5

Or

50 = 2 x 5²

• Taking root on both the sides we get;

√50 = √(5 × 5 × 2) = 5√2

• Since, the value of √2 = 1.414, approximately, thus,

√50 = 5 × 1.414 = 7.07

• Therefore, the square root of 50 is approximately 7.07.

Long Division Method

As we know, 50 is not a perfect square. Thus, the square root of 50 is not a whole number, but a fraction. To find the accurate value of √50 we have to use the long division method. Follow the below steps.

• Step 1: Put a decimal after 50 followed by three pairs of zeroes.
• Step 2: Pair the digits and put a bar over the digits from left to right.
• Step 3: Now, taking 50 as a dividend, think of a number that can be multiplied by itself to get a value equal to or less than 50. 7 x 7 = 49. Thus, 7 is the quotient.
• Step 4: Put decimal after 7, to divide the rest of the zeros after the decimal in the dividend part.
• Step 5: Add 7 to the previous divisor to get a new divisor. 7 + 7 = 14.
• Step 6: Taking 14 as a divisor, think of a digit (A) that can be placed next to 14, such that 14A multiplied by X will give a value less than or equal to 100. 140 x 0 = 0. Thus, at the quotient part, we have 7.0.
• Step 7: Again, add 0 to 140 to get the next divisor and write down the two zeros next 100.
• Step 8: Think of a digit that can be placed next to 140 (say Y), such that 140Y multiplied by Y, results in a value less than or equal to 10000. So, 1407 x 7 = 9849.
• Step 9: The quotient is 7.07. We can perform the same step repeatedly to get a more accurate value.

Hence, the square root of 50 up to two places of decimal is 7.07.

Repeated Subtraction Method for Root 50

This method is applicable to the square root of perfect squares. Since, 50 is not a perfect square, we cannot determine the square root using repeated subtraction method.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

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Solved Examples

Q.1: If the area of a square is equal to 50 sq. units. Find the length of the side of the square.

Solution: Given, area of square = √50 sq. unit

As we know, area of square = side²

So, side = √(area of square)

Hence, the required side length is √50 units or 5√2 units.

Q.2: Simplify √100 x √50. Write the answer in radical form.

Solution: Given,

√100 x √50

100 = 10 x 10

50 = 2 x 5 x 5

Therefore,

√100 x √50 = √(10 x 10) x √(2 x 5 x 5)

= 10 x 5√2

= 50√2