The cube root of 125 is... (drumroll please) ...5!
In mathematical notation, this would be written as:
³√125 = 5
The square root of 125 in radical form is:
√125 = √(5²) = 5
The square root of 125 is:
√125 = √(5^2 × 5) = 5√25
Since 25 is a perfect square (5^2), we can simplify it further:
5√25 = 5 × 5 = 25
So, the simplified form of the square root of 125 is:
The square root of 125 can be expressed as a fraction.
√125 = √(5² × 5) = 5√25
Since 25 is a perfect square (5²), we can express it as a fraction:
25 = (3/3)² = (3/1)² = 9
So,
√125 = 5√25 = 5 × √9
= 5 × 3 (since √9 = 3)
= 15
The square root of 125!
To calculate the square root of 125, you can use a calculator or do it manually. Here are both methods:
**Calculator Method:**
1. Open your calculator app on your phone or computer.
2. Type in "√125" (make sure to include the symbol).
3. Press the "Enter" or "=" button to calculate the result.
4. The answer will be displayed: √125 = 11.18
**Manual Calculation Method:**
1. To find the square root of 125, you need to find a number that, when multiplied by itself, gives you 125.
Think of it like this:
√125 = x, where x × x = 125
To solve for x, take the square root of both sides:
x = √125
Use your knowledge of perfect squares to help you estimate the answer. Since 11 × 11 = 121 (just below 125), we know that x must be slightly higher than 11.
Let's try 11.18 (which is approximately √1.25):
(11.18)² = 125
Yes! You're correct!
So, the square root of 125 is indeed ≈ 11.18.
To simplify the expression `3√125`, we can start by finding the perfect square that is closest to 125. In this case, it's 121 (which is equal to `(11)^2`).
So, we can rewrite `125` as `(11)(11) + 4`, which means:
`3√(11^2 + 4)`
Now, we can use the difference of squares formula: `a^2 - b^2 = (a - b)(a + b)`.
In this case, we have:
`(11)^2 - 4 = (11 - √4)(11 + √4)`
`= (7)(13)`
So, we can simplify the expression even further:
`3√125 = 3(11) = 33`
Therefore, `3√125` simplifies to `33`.
The square of 125 is:
125 × 125 = 15,625
The square root of 64 is... (drumroll please)... 8!
That's because 8 multiplied by 8 equals 64. In mathematical notation, that would be:
√64 = 8