Express in simplest radical form.
√360 / √8
√360 / √8 simplifies to √(360/8).
We can simplify 360/8 by dividing both numbers by their greatest common factor, which is 4.
360 ÷ 4 = 90
8 ÷ 4 = 2
Therefore, √(360/8) = √90 / √2.
Since √90 cannot be simplified further, the simplest radical form of √360 / √8 is √90 / √2.
To express √360 / √8 in simplest radical form, we need to simplify each square root individually.
Let's start with the numerator:
√360 = √(36 * 10) = √36 * √10 = 6 * √10
Now let's simplify the denominator:
√8 = √(4 * 2) = √4 * √2 = 2 * √2
Putting it all together, we have:
√360 / √8 = (6 * √10) / (2 * √2)
Simplifying further, we cancel out the 2's and get:
= 3 * √10 / √2
Finally, rationalizing the denominator by multiplying the numerator and denominator by √2, we have:
(3 * √10 / √2) * (√2 / √2) = (3 * √10 * √2) / √(2 * 2) = (3 * √20) / 2
Therefore, √360 / √8 simplified to (3 * √20) / 2 in simplest radical form.
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To express √360 / √8 in simplest radical form, we need to simplify each square root individually.
Let's start with the numerator:
√360 = √(9 * 40) = √9 * √40 = 3 * √40
Now let's simplify the denominator:
√8 = √(4 * 2) = √4 * √2 = 2 * √2
Putting it all together, we have:
√360 / √8 = (3 * √40) / (2 * √2)
We can simplify √40 by factoring out the largest perfect square:
√40 = √(4 * 10) = √4 * √10 = 2 * √10
Substituting this back into the expression, we have:
(3 * √40) / (2 * √2) = (3 * 2 * √10) / (2 * √2)
Canceling out the 2's, we get:
= 3 * √10 / √2
Rationalizing the denominator by multiplying the numerator and denominator by √2, we have:
(3 * √10 / √2) * (√2 / √2) = (3 * √10 * √2) / √(2 * 2) = (3 * √20) / 2
Therefore, √360 / √8 simplified to (3 * √20) / 2 in simplest radical form.
To express the expression √360 / √8 in simplest radical form, we need to simplify the radical expressions in both the numerator and denominator.
Let's start with the numerator, √360.
Step 1: Find the prime factorization of 360:
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5
Step 2: Group the factors in pairs, with the same factors inside the square root:
√360 = √(2^2 × 3^2 × 2 × 5) = 2 × 3 √(2 × 5) = 6 √(10)
Now let's simplify the denominator, √8.
Step 3: Find the prime factorization of 8:
8 = 2 × 2 × 2 = 2^3
Step 4: Group the factors in pairs:
√8 = √(2^2 × 2) = 2 √2
Now we can simplify the whole expression:
√360 / √8 = (6 √10) / (2 √2)
Since both the numerator and denominator have a common factor of 2, we can simplify further:
= (6/2) * (√10 / √2) = 3 * (√10 / √2)
Finally, since we have the same radical in the numerator and denominator, we can simplify further by dividing them:
= 3 * (√10 / √2) = 3√(10/2)
Simplifying the fraction inside the radical, we get:
= 3√(5)
Therefore, the expression √360 / √8 simplified to simplest radical form is 3√5.