Square root of 125

Square root of 125 is equal to 5√5 in radical form and 11.1803398875 in decimal form. When we multiply the square root value to itself, it results in the original number. Thus, square root is the inverse method of squaring a number.

The square root of 125 is denoted by √125, where ‘√’ is the radical symbol and 125 is the radicand.

125 is an imperfect square therefore, the square root of 125 will not be a whole number. Using prime factorisation, we can get the square root of the imperfect number in a radical form. But to find the exact square root, we can use the long division method.

Also check:

• Find Square Root Of Decimals
• Square Root 1 to 100
• Square Root Of A Number By Repeated Subtraction
• Square Root Tricks

How to Find the Square root of 125?

Since we know, √5 is an irrational number, therefore, √125 = 5√5 is also an irrational number. Therefore, we cannot represent the square root of the irrational number in the form of P/Q, where P is the numerator and Q is the denominator. Let us see, how can we find the square root of 125.

We can use two methods here to find the √125.

• Prime Factorisation Method
• Long Division Method

Prime Factorisation Method

In the prime factorisation method, we can write the number, 125, in the form of a product of prime factors. Hence,

125 = 5 x 5 x 5

Now, we have to check how many prime factors can be paired to make square terms.

125 = (5 x 5) x 5

So, there is only one pair of prime factors that can be squared.

125 = 5² x 5

Now we take the square root of the numbers both the sides we get:

We can cancel the square term with the square root.

√125 = 5√5

Thus, this is the value of √125.

Since, the value of √5 = 2.2360679775

Therefore, 5√5 = 5 x 2.2360679775 = 11.1803398875

Finally, the value of square root of 125 is:

√125 = 11.1803398875

Long Division Method

Since, we know, 125 is not a perfect square, therefore, to find the accurate value of √125, we can use the long division method. We can find the square root of 125 upto three places of decimal here.

Therefore, the square root of 125 is equal to 11.18, approximately.

Can we use the Repeated Subtraction Method?

We cannot use the repeated subtraction method to find the square root of 125, because 125 is not a perfect square. In this method, we start subtracting the original number with the increasing order of odd numbers, until we get zero. Then, the number of times the subtraction is done is the required square root.

Let us try.

• 125 – 1 = 124
• 124 – 3 = 121
• 121 – 5 = 116
• 116 – 7 = 109
• 109 – 9 = 100
• 100 – 11 = 89
• 89 – 13 = 76
• 76 – 15 = 61
• 61 – 17 = 44
• 44 – 19 = 25
• 25 – 21 = 4
• 4 – 23 = -19

Thus, since we didn’t get zero at the end, hence this method cannot be used.

Square Roots of Perfect Numbers

• Square root of 100 = 10
• Square root of 121 = 11
• Square root of 81 = 9
• Square root of 25 = 5
• Square root of 169 = 13
• Square root of 225 = 15

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Solved Examples

Q.1: Rationalise the denominator: 1/5√5.

Solution: Given, 1/5√5

To rationalize the denominator, we need to remove the radical term. Thus, multiplying numerator and denominator by √5, we get;

⇒ √5/25

Hence, is the answer.

Q.2: Find the area of a square yard whose side is equal to 5√5 feet, each.

Solution: Given, the side of the square is 5√5 feet.

As we know,

Area of the square yard = (length of the side)²

Area = 5√5²

Area = 125 sq.ft.

Therefore, the area of the square yard is 125 sq.ft.

Q.3: How to find the cube root of 125?

Solution: 125 is a perfect cube. Hence, by prime factorisation of 125, we get;

125 = 5 x 5 x 5

125 = 5³

Now, taking the cube root on both the sides;

³√125 = ³√5³

Cube root and cube of the number, gets cancelled.

³√125 = 5

Hence, the cube root of 125 is 5.

Q.4: What is the value of (√125)³?

Solution: The value of (√125)³ is:

(√125)³ = (5√5)³

= 5³ x (√5)³

= 125 x (√5 x √5 x √5)

= 125 x 5√5

= 625√5

We can further simplify by using the value √5=1.7 (approx)

(√125)³ = 625 x 1.7 = 1062.5

Hence, is the answer.

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