Square root of 125 is same to 5√5 in radical type and 11.1803398875 in decimal form. As soon as we multiply the square root value to itself, it outcomes in the initial number. Thus, square source is the inverse technique of squaring a number.

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

 Square source of 125 = √125 = ±5√5OrIn decimal form,√125 = 11.1803398875OrIn Exponent Form,(125)½ = 11.1803398875

125 is an imperfect square therefore, the square root of 125 will not be a entirety number. Utilizing prime factorisation, we can gain the square root of the imperfect number in a radical form. But to uncover the exact square root, we have the right to use the long department method.

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## How to uncover the Square source of 125?

Since us 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, whereby P is the numerator and Q is the denominator. Let united state see, how deserve to we uncover the square root of 125.

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

Prime Factorisation MethodLong division Method

### Prime Factorisation Method

In the element factorisation method, we deserve to write the number, 125, in the kind of a product of element factors. Hence,

125 = 5 x 5 x 5

Now, we have to check how numerous prime factors can be combine to do square terms.

125 = (5 x 5) x 5

So, over there is just one pair the prime determinants that can be squared.

125 = 52 x 5

Now us take the square root of the number both the sides we get:

(sqrt125 = sqrt5^2 imes sqrt5)

We can cancel the square term with the square root.

√125 = 5√5

Thus, this is the worth of √125.

Since, the value of √5 = 2.2360679775

Therefore, 5√5 = 5 x 2.2360679775 = 11.1803398875

Finally, the value of square source of 125 is:

√125 = 11.1803398875

 Facts:Square source of 125 is a not a natural or a totality number yet an irrational number125 is an odd composite number125 is one imperfect square, hence no herbal number have the right to be squared to acquire the original number125 is a perfect cube, (125 = 53) hence the cube source of 125 is 5.The root of 125 are +5√5 or -5√5

### Long division Method

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

Therefore, the square source of 125 is same to 11.18, approximately.

### Can we use the repeated Subtraction Method?

We cannot use the repetitive subtraction technique to find the square source of 125, due to the fact that 125 is not a perfect square. In this method, we start subtracting the initial number with the increasing order of weird numbers, till we acquire zero. Then, the variety of times the individually is excellent is the compelled square root.

Let united state try.

125 – 1 = 124124 – 3 = 121121 – 5 = 116116 – 7 = 109109 – 9 = 100100 – 11 = 8989 – 13 = 7676 – 15 = 6161 – 17 = 4444 – 19 = 2525 – 21 = 44 – 23 = -19

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

### Square root of Perfect Numbers

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

## Solved Examples

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

Solution: Given, 1/5√5

To rationalize the denominator, we must remove the radical term. Thus, multiply numerator and also denominator by √5, us get;

⇒ (frac15sqrt5 imes fracsqrt5sqrt5)⇒ (fracsqrt55 imes 5)⇒ √5/25

Q.2: find the area the a square garden whose side is same to 5√5 feet, each.

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

As we know,

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

Area = 5√52

Area = 125 sq.ft.

Therefore, the area that the square garden is 125 sq.ft.

Q.3: how to uncover the cube source of 125?

Solution: 125 is a perfect cube. Hence, by prime factorisation that 125, us get;

125 = 5 x 5 x 5

125 = 53

Now, acquisition the cube source on both the sides;

3√125 = 3√53

Cube root and also cube of the number, it s okay cancelled.

3√125 = 5

Hence, the cube source 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 additional simplify by using the value √5=1.7 (approx)

(√125)3 = 625 x 1.7 = 1062.5