Divide 410√/2√ . Provide an exact answer
To divide √410 by √2, we can rationalize the denominator.
We multiply both the numerator and denominator by √2 to rationalize the denominator:
(√410 * √2) / (√2 * √2)
= (√(410 * 2)) / (2)
= (√820) / 2
Therefore, the exact answer is (√820) / 2.
To divide the expression (410√) by (2√) and obtain an exact answer, we can simplify the expression by rationalizing the denominators. Rationalizing the denominator means eliminating any radicals (square roots) from the denominator.
Let's break down the steps:
Step 1: Simplify the numerator and denominator separately.
The numerator (410√) has no simplification since it does not have a perfect square (√) within it.
The denominator (2√) is already in simplified form but can be rationalized.
Step 2: Rationalize the denominator.
To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of (2√) is (2√).
Multiplying the numerator and the denominator by the conjugate, we get:
(410√) / (2√) * (2√) / (2√)
Simplifying the expression, we have:
(820√) / (2 * √ * √)
(820√) / (2 * √²)
(820√) / (2 * (√(√))²)
(820√) / (2 * (√2)²)
(820√) / (2 * 2)
(820√) / 4
205√
So, the exact answer after dividing (410√) by (2√) is 205√.
To divide 410√ by 2√, you need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of 2√, which is 2√.
The conjugate of 2√ is 2√.
So, multiplying both the numerator and denominator by 2√, we get:
(410√)/(2√) = (410√ * 2√)/(2√ * 2√)
Simplifying, we have:
(820√^2)/(2^2√^2)
= (820*2)/(2*2)
= 1640/4
= 410
Therefore, the exact answer is 410.
Divide 4√10/√2
To divide 4√10 by √2, we need to rationalize the denominator.
First, let's simplify the numerator: 4√10.
Next, let's rationalize the denominator: √2.
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of √2, which is also √2. Multiplying the expression by √2/√2, we get:
(4√10 * √2) / (√2 * √2)
= (4√(10 * 2)) / (√(2 * 2))
= (4√20) / √4
= (4√20) / 2
= 2√20
= 2 * √(4 * 5)
= 2 * √(20)
= 2 * √(4 * 5)
= 2 * 2√5
= 4√5
Therefore, the exact answer is 4√5.
Simplify 300−−−√ .(1 point)
To simplify √300, we can factorize 300 and find perfect square factors:
300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2
Taking the square root of the perfect square factors:
√300 = √(2^2 * 3 * 5^2) = 2 * √(3 * 5^2) = 2 * 5 √3 = 10√3
So, √300 simplifies to 10√3.