divide 98 as irrational number / 3 as radicand and 5 as radical
To divide 98 by an irrational number, we need to specify which irrational number to use. Let's use the square root of 3 (√3) as the irrational number.
To find the division of 98 by √3, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is √3.
98 / √3 = (98 * √3) / (√3 * √3)
= (98√3) / 3
= (98/3) * √3
So, dividing 98 as an irrational number by 3 as the radicand gives us (98/3)√3.
Now, let's divide 5 by a radical, √3.
5 / √3 = (5 * √3) / (√3 * √3)
= (5√3) / 3
Therefore, dividing 5 by √3 gives us (5/3)√3.
To divide 98 as an irrational number by 3 as the radicand and 5 as the radical, we can follow these steps:
Step 1: Express 98 as an irrational number:
98 can be expressed as the product of two irrational numbers: 7√2. To find this, we need to find the prime factorization of 98, which is 2 * 7 * 7. We can then take the square root of the prime factors of 98 and rewrite them as irrational numbers.
So, 98 can be expressed as 7√2.
Step 2: Divide 7√2 by the radicand, which is 3:
To divide by a radicand, we divide the coefficient (number outside the radical) and simplify the radical.
Divide 7 by 3: 7/3.
Simplify the radical: √2.
Therefore, 7√2 / 3 simplifies to (7/3)√2.
Step 3: Divide by the radical, which is 5:
To divide by a radical, we multiply the coefficients and simplify the radical.
Multiply (7/3) by 5: (7/3) * 5 = 35/3.
Simplify the radical: √2.
Therefore, (7/3)√2 / 5 simplifies to (35/3)√2 / 5.
Step 4: Final simplification:
We can simplify the expression further by multiplying the two fractions together:
(35/3) * (√2 / 5) = (35√2) / (3 * 5) = (35√2) / 15.
So, the final result is (35√2) / 15.
To divide 98 by an irrational number (let's call it x), we need to express 98 as the radicand (the number inside the radical) and x as the radical. Here's how you can do it:
Step 1: Express 98 as the radicand.
To express 98 as the radicand, we need to find an irrational number whose square is equal to 98. We know that the square root of 98 (√98) is not an integer, so it is an irrational number.
Step 2: Express 3 as the radical.
To express 3 as the radical, we simply write it as √3.
Step 3: Express 5 as the radical.
To express 5 as the radical, we write it as √5.
Now, putting it together, we have:
98 ÷ (√3 * √5)
To simplify this expression, we can multiply both the numerator and denominator by (√3 * √5) to eliminate the radicals in the denominator.
98 * (√3 * √5) ÷ (√3 * √5 * √3 * √5)
Simplifying further, we get:
98√15 ÷ (3 * 5)
Which becomes:
98√15 ÷ 15
So the final result is 98√15 ÷ 15.
√98/3√5
To divide √98 by 3√5, we can simplify by rationalizing the denominator.
First, let's simplify √98:
√98 = √(2 * 49) = √2 * √49 = 7√2.
Now, we can rewrite the division expression as:
(7√2) / (3√5).
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator (√5):
[(7√2) / (3√5)] * [(√5) / (√5)].
This simplifies to:
(7√2√5) / (3√5√5) = (7√10) / (3 * 5) = (7√10) / 15.
Thus, the final result is (7√10) / 15.
no give n exct answer
Apologies for the confusion. Let's calculate the exact answer without any approximate decimal values.
To divide √98 by 3√5, we can simplify it as follows:
√98 / 3√5
First, let's simplify the radicands:
√98 = √(2 * 7^2) = 7√2
√5 = √5
Now, we can rewrite the division expression as:
(7√2) / (3√5)
To divide these expressions, we can multiply the numerator and denominator by the conjugate of the denominator:
[(7√2) / (3√5)] * [(√5) / (√5)]
This simplifies to:
(7√2 * √5) / (3√5 * √5)
Multiplying the square roots:
(7√10) / (3 * 5)
Simplifying:
(7√10) / 15
Therefore, the exact answer is (7√10) / 15.