The square root of 125 can be expressed as a fraction. To do this, we need to find the perfect square that is equal to or less than 125.
Let's start by finding the square root of 125:
√125 = √(5^2 × 5)
Since 5^2 = 25, we can simplify the expression:
√125 = √(25 × 5)
= √25 × √5
= 5√5
Now, to express this as a fraction, we need to find an equivalent fraction that has a perfect square in its numerator and denominator.
Here's one way to do it:
√125 = 5√5 = (25/1)^(1/2)
= (25/1) × (√5/5)
= (25√5)/5
So, the square root of 125 as a fraction is:
(25√5)/5
The square root of 125 in radical form is:
√125 = √(5²) = 5
The square root of 125!
The square root of 125, denoted as √125, is a mathematical operation that finds the number that, when multiplied by itself, gives 125. In other words:
√125 = x, where x^2 = 125
To find the square root of 125, you can use various methods, including:
1. **Prime factorization**: Find the prime factors of 125: 5 × 5 × 5. Then, take the square root of each factor: √25 = 5 and √5 = √5 (since 5 is a perfect square). So, √125 = √(5 × 5 × 5) = √5 × √5 × √5 = 5√5.
2. **Approximation**: Use an approximate value for the square root of 125. One way is to use the formula: √x ≈ (x^0.5). Plugging in x = 125, you get: √125 ≈ (125^0.5) ≈ 11.18.
So, the exact value of √125 is:
√125 = 5√5 = 5 × 1.5811388316939317 (approximately)
Keep in mind that the square root of a perfect square (like 125) can be expressed as a simple fraction, whereas the square root of an imperfect square (e.g., √16) cannot be simplified further.
Do you have any specific questions about the square root of 125 or would you like to explore more mathematical concepts?
You want to know how to calculate the square root of 125 using a calculator!
A square root is a mathematical operation that finds a value that, when multiplied by itself, gives a specified number. In this case, you want to find the square root of 125.
Using a calculator, you can simply type in the expression:
√125
And press "Enter" or "=" (depending on your calculator model). The calculator will then display the result:
√125 = 11.18 (approximately)
So, the square root of 125 is approximately 11.18!
Note that calculators can give more precise results than you might get by doing the calculation manually using a formula like:
√x = y, where y^2 = x
But for most practical purposes, the calculator's result should be close enough!
To simplify the expression, we can start by finding the perfect square that is closest to 125. In this case, it's 121 (which is the square of 11).
So, we can rewrite the expression as:
√(125) = √(121 + 4)
Now, we can use the fact that the square root of a sum is equal to the difference between the squares of the two numbers:
√(125) = √((11)^2 + 4)
= |11| √((11)^2 + 4)
= 11 √(1 + (4/121))
= 11 √(129/121)
Simplifying further, we get:
√(125) = 11 × √(1.07) ≈ 11.15
So, the simplified form of the expression is approximately 11.15.
To find the square root of 125 using the division method, you can follow these steps:
1. Write down the number whose square root you want to find: 125
2. Divide the number by a perfect square that is close to it. In this case, let's start with 10 (which is a perfect square because 10 = 3^2).
125 ÷ 10 = 12.5
This means that 10 is not the exact square root of 125, so you need to try a larger perfect square.
3. Divide the result by another perfect square that is close to it. Let's try 11 (which is also a perfect square because 11 = 1^2).
12.5 ÷ 11 = 1.136...
Since this is still not an exact value, you can continue dividing by larger perfect squares until you get a value that is close enough.
4. After a few iterations, you might find that:
125 ÷ 121 = 1.025
This means that the square root of 125 is approximately equal to 11.18 (since √(12.25) ≈ 11.18).
So, using the division method, we can estimate the square root of 125 as:
√125 ≈ 11.18
The square root of 64 is... (drumroll please)... 8!
That's because 8 × 8 = 64.
A perfect square is an integer that can be expressed as the square of another integer, i.e., it has the form n^2 for some integer n.
The square root of 125 is approximately 11.1805 (since √125 = √(5^3) = 5√25 = 5 × 5 = 25).
Since we cannot express 125 as a perfect square of an integer (e.g., 11^2 = 121, not 125), we can conclude that **125 is NOT a perfect square**.