What Is The Square Root Of 125: A Simple Explanation

What is square root 125 simplified?

Square root of 125 is equal to 5√5 in radical form and 11.1803398875 in decimal form.

What is the square of 125?

Square of 125: 15,625 What Is the Square Root of 125?

Is 125 a perfect square Why?

Since 125 can’t be the square of another integer, it is not a perfect square number.

What are the factors of 125?

What are the factors of 125? The factors of 125 are the numbers that divide 125 exactly, leaving the remainder as zero. The number 125 is exactly divisible by 1, 5, 25 and 125 only. So, the factors of 125 are 1, 5, 25 and 125.

Is 125 a perfect cube?

125 = 5 × 5 × 5 = 5 3 . Therefore, 125 is a perfect cube.

How to simplify 4 √ 125?

As we have obtained the quotient as a prime number, so we will not divide the number further. But, we will take out 1 factor from the pair of common factors in order to find the square root. Hence, 4 square roots of 125 can be simplified as 20 square roots of 5. Thus, this is the required answer.

What is the value of √ 125 √ 5?

Expert-Verified Answer The product of √125 × √5 = 25. Hence the product we get of the question √125 × √5 is 25 or (5)².

What can I multiply to get 125?

When you multiply any two whole numbers with each other and get 125 as the answer, you can say that both the numbers will be the factors of 125. 1× 125 = 125 and 5 × 25 = 125; thus, the factors of 125 are 1, 5, 25, and 125.

Is 125 a square number yes or no?

Explanation: No, 125 is not a perfect square. In mathematics, a perfect square is a number that can be expressed as the product of a whole number multiplied by itself. For example, 9 is a perfect square because it can be expressed as 3 * 3.

Is 0 a perfect square?

Since zero satisfies all the definitions of squares, it is considered as a perfect square.

Is 9 a square number?

The first ten square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Is 27 a perfect cube?

So, the cube root is cancelled by the cube of 3. Hence, the value of the cube root of 27 is equal to 3. Also, we can say that 27 is a perfect cube number since its cube root value is a whole number.

What is a value of √5?

Therefore, the value of root 5 is, √5 = 2.2360… You can find the value of the square root of all the non-perfect square number with the help of the long division method.

Is 125 a multiple of 125?

The first 10 multiples of 125 are 125, 250, 375, 500, 625, 750, 875, 1000, 1125 and 1250.

Is 125 divisible by?

The number 125 is divisible by 1, 5, 25, 125.

Is 8 a perfect cube?

A perfect cube is the cube of a whole number, found by multiplying a whole number by itself three times. For example, the number 8 is a perfect cube because 2 × 2 × 2 = 8 .

Is 1000 a perfect cube?

A perfect cube is a number which is the cube of an integer. Since the cube of 10 is 1000, 1000 is a perfect cube number.

Is 3 √125 rational?

Therefore, the value of the cube root of 125 is an integer (rational).

Can 125 be a perfect square?

125 is NOT a perfect square, because there is no whole number that multiplies by itself to give 125.

Why is 5 cubed 125?

When a number has three equal prime factors, the cube root is that prime factor. 125 is equal to 25 times five and 25 is equal to five times five. So technically, 125 is equal to five times five times five, which means five cubed is equal to 125.

Which whole number is closest to √125?

Expert-Verified Answer The square root of 125 is closest to the whole number 11, since 11 squared is 121 and is the nearest perfect square to 125.

How to simplify a square root?

Step 1: Find the prime factors of the number inside the radical sign. Step 2: Group the factors into pairs. Step 3: Pull out one integer outside the radical sign for each pair. Leave the other integers that could not be paired inside the radical sign.

What is the simplified form of √ 125 √ 125 √ 845?

Answer: After simplifying the expression √125 + √125 – √845 , we get -3 √5. Therefore, after simplifying the expression √125 + √125 – √845 , we get -3 √5.

What is 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.

Is 125 a perfect square?

125 is not a perfect square; hence its square root is an irrational number. This concludes that the square root of any number “n,” which is not a perfect square, will always be an irrational number. The square root of 125 in the radical form is expressed as 5√5.

What is the second root of 125?

To sum up, the square roots of 125 are ±11.1803398875; the positive real value is the principal. Finding the second root of the number 125 is the inverse operation of rising the ²√125 to the power of 2. That is to say, (±11.1803398875) 2 = 125. Further information about the root of a number like ²√125 can be found on our page n-th Root.

Can 125 be simplified?

125 can be simplified only if you can make 125 inside the radical symbol smaller. This is a process that is called simplifying the surd. In this example, the square root of 125 can be simplified. √125 = 5√5. If you have a calculator then the simplest way to calculate the square root of 125 is to use that calculator.

Alright, let’s dive into the world of square roots and figure out what the square root of 125 is.

You see, the square root of a number is like finding a number that, when multiplied by itself, gives you the original number. Think of it like solving a puzzle – we’re looking for the missing piece that makes the equation work.

In this case, we’re searching for a number that, when multiplied by itself, equals 125. We can represent this with the following equation:

x * x = 125

Now, you might be thinking, “This seems tricky! How do I find that number?” Don’t worry, we’ll get there. Let’s break this down.

Finding the Square Root of 125

There are a few ways to figure out the square root of 125. One approach is to use a calculator. Most calculators have a square root function, often denoted by a radical symbol (√). Just enter 125 and press the square root button – and voila! You’ll get the answer.

But what if you don’t have a calculator handy? Let’s explore another way – using prime factorization.

Prime Factorization Approach

Prime factorization is like breaking down a number into its smallest building blocks – its prime factors. Prime factors are numbers that can only be divided by 1 and themselves. Think of them as the Lego bricks of numbers.

1. Break down 125: We can start by dividing 125 by 5. 125 / 5 = 25. Then, we can divide 25 by 5 again. 25 / 5 = 5.

2. Identify the prime factors: We’ve found that 125 can be expressed as 5 * 5 * 5.

3. Find pairs: Notice that we have three 5s. If we take two of them (5 * 5) we get 25.

4. Square root: The square root of 125 is 5√5. Why? Because 5 * 5 = 25 and 25 * 5 = 125.

Let’s try to visualize this with a table:

| Number | Prime Factors | Pairs | Square Root |
| :——– | :—————– | :—— | :————- |
| 125 | 5 * 5 * 5 | 5 * 5 | 5√5 |

Simplifying the Square Root

Now, you might be thinking, “5√5 – what does that mean?” Well, it’s an irrational number. This means it can’t be expressed as a simple fraction. 5√5 represents the exact value of the square root of 125.

However, if you need an approximate value, you can use your calculator to find the decimal representation of 5√5. It’s approximately 11.18.

Understanding Square Roots

So, we’ve found that the square root of 125 is 5√5 or approximately 11.18. Understanding square roots is useful for many things in math and science. Let’s look at some examples:

Area calculations: Finding the area of a square involves squaring its side length. So, if you know the area of a square is 125 square units, you can find its side length by calculating the square root of 125 (5√5 units).
Pythagorean theorem: The Pythagorean theorem relates the sides of a right triangle. It states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Square roots are used to solve for unknown side lengths in right triangles.
Algebraic equations: Square roots often appear in algebraic equations. They can be used to solve for unknown variables.

The Importance of Understanding Square Roots

Understanding square roots is like having a handy tool in your mathematical toolbox. They’re used in various applications, from geometry and algebra to physics and engineering.

FAQs About the Square Root of 125

Here are some common questions about the square root of 125:

Q: Is the square root of 125 a rational or irrational number?
A: The square root of 125 is an irrational number. It can’t be expressed as a simple fraction.

Q: What is the decimal representation of the square root of 125?
A: The decimal representation of the square root of 125 is approximately 11.18.

Q: How can I find the square root of 125 without a calculator?
A: You can use prime factorization to find the square root of 125. Break down 125 into its prime factors (5 * 5 * 5), find pairs of prime factors (5 * 5), and then express the square root as 5√5.

Q: Why is the square root of 125 important?
A: Understanding square roots is essential for solving problems in various areas of mathematics, science, and engineering. They’re used in area calculations, the Pythagorean theorem, algebraic equations, and many other applications.

Q: What is the square root of 125 squared?
A: The square root of 125 squared is 125. Squaring and taking the square root are inverse operations.

Q: What is the square root of 125 cubed?
A: The square root of 125 cubed is 125 * √5. Here’s why: 125 cubed is 125 * 125 * 125. We can rewrite this as (5 * 5 * 5) * (5 * 5 * 5) * (5 * 5 * 5), which simplifies to 5^9. Taking the square root of 5^9 gives us 5^(9/2), which can be simplified to 5^4 * √5, or 125 * √5.

Hopefully, this explanation has helped you understand what the square root of 125 is and why it’s important. Remember, mathematics is full of fascinating concepts, and understanding them can open doors to new insights and problem-solving skills. Keep exploring!

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