Express in simplest radical form.
start fraction, square root of, 40, end square root, divided by, 6, end fraction
6__
40
To express this in simplest radical form, we need to simplify the square root of 40.
Since 40 can be simplified, we can rewrite it as 4 times 10: √40 = √(4 * 10).
The square root of 4 is 2, so this becomes: 2√10.
So, the expression in simplest radical form is 2√10 divided by 6.
To simplify the expression, we first need to find the largest perfect square that can be factorized from both the numerator and the denominator.
The largest perfect square that can be factorized from both 40 and 6 is 4. Therefore, we will simplify the expression as follows:
square root of (40) / 6 is equal to (square root of (4 * 10)) / 6
Now, we can simplify further:
(square root of (4) * square root of (10)) / 6
The square root of 4 is 2, so the expression becomes:
(2 * square root of (10)) / 6
Finally, we can simplify by dividing both the numerator and the denominator by 2:
2 * square root of (10) / 2 = square root of (10)
Therefore, the expression simplified in simplest radical form is square root of (10).
To express the given fraction in simplest radical form, we need to simplify the square root of 40.
First, let's prime factorize 40: 40 = 2 * 2 * 2 * 5.
Now we can rewrite the fraction as:
Start Fraction square root of (2 * 2 * 2 * 5) divided by 6 End Fraction.
We can simplify the square root by separating the factors into two square roots:
Start Fraction (square root of 2 * 2) * (square root of 2 * 5) divided by 6 End Fraction.
The square root of 2 * 2 is equal to 2, so we can simplify further:
Start Fraction 2 * (square root of 2 * 5) divided by 6 End Fraction.
Now we simplify the fraction by canceling out common factors:
2/6
We can simplify the fraction 2/6 by dividing both the numerator and denominator by 2:
1/3.
Therefore, the expression in simplest radical form is: 1/3.
Can u give it to me more understanding
Certainly! Let's simplify the expression step by step to make it more understandable.
The expression is Start Fraction square root of 40 divided by 6 End Fraction.
First, let's simplify the square root of 40.
To do this, we can break down 40 into its prime factors: 40 = 2 * 2 * 2 * 5.
Now, let's rewrite the expression with the prime factors: Start Fraction square root of (2 * 2 * 2 * 5) divided by 6 End Fraction.
We can group the prime factors that appear twice inside the square root sign: Start Fraction (square root of 2 * 2) * (square root of 2 * 5) divided by 6 End Fraction.
The square root of 2 * 2 simplifies to 2, so we can simplify further: Start Fraction 2 * (square root of 2 * 5) divided by 6 End Fraction.
Now, let's simplify the fraction by canceling out common factors.
The numerator (2) and the denominator (6) are both divisible by 2.
Dividing both the numerator and denominator by 2, we have: Start Fraction 1 * (square root of 2 * 5) divided by 3 End Fraction.
Simplifying further, we get: Start Fraction square root of 10 divided by 3 End Fraction.
Therefore, the expression in simplest radical form is: square root of 10 divided by 3.