√98/3√5
To simplify the expression √98/3√5, we can simplify the individual square roots and then divide:
√98 = √(49 * 2) = 7√2
3√5 remains the same.
Now we can divide the two square roots:
(7√2) / (3√5)
This cannot be simplified any further, so the final answer is (7√2) / (3√5).
To simplify the expression √98/3√5, we can first simplify the numerator and the denominator separately.
Let's start with the numerator, √98.
To simplify the square root of 98, we need to find the largest perfect square that is a factor of 98. The largest perfect square that divides 98 is 49, which is equal to 7^2.
So, √98 = √(7^2 * 2) = 7√2.
Now let's simplify the denominator, 3√5.
Since there is no perfect square that divides 5, we cannot simplify it further.
Now we can rewrite the original expression:
√98/3√5 = (7√2)/(3√5).
To simplify this expression further, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is (√5).
(7√2)/(3√5) * (√5)/(√5) = (7√10√5)/(3√5√5).
Simplifying further, we get:
(7√10√5)/(3√5√5) = (7√10)/(3√5).
To simplify the given expression, √98 / 3√5, we need to rationalize the denominator. To do this, we multiply both the numerator and the denominator by the conjugate of the denominator.
The conjugate of 3√5 is -3√5 (changing the sign from positive to negative). Therefore, we multiply both the numerator and the denominator by -3√5.
(-3√5 * √98) / (-3√5 * 3√5)
In the numerator:
-3√5 * √98 = -3 * √(5 * 98) = -3 * √(5 * 49 * 2) = -3 * √(7² * 2) = -3 * 7 √2 = -21√2
In the denominator:
-3√5 * 3√5 = -3 * 3 * √(5 * 5) = -3 * 3 * 5 = -45
So, the simplified expression is -21√2 / -45.
Now, we can further simplify this by canceling out the common factors in the numerator and denominator. In this case, there is no common factor other than 1.
Therefore, the final simplified expression is:
-21√2 / -45 = 21√2 / 45
So, √98 / 3√5 simplifies to 21√2 / 45.