Divide 86√2 . Provide an exact answer.(1 point)
To divide 86√2, you'll need to divide both the number and the square root separately.
First, divide 86 by 2, which gives you 43. Then, divide √2 by √2, which equals 1.
Therefore, 86√2 divided by √2 is equal to 43.
To divide 86√2, we can multiply the numerator and denominator by the conjugate of √2, which is also √2:
(86√2)(√2) = 86(√2)(√2) = 86(√2 * √2) = 86(√(2*2)) = 86(√4) = 86(2) = 172
Therefore, the exact answer of the division 86√2 is 172.
To divide 86√2, you can start by rationalizing the denominator. This means getting rid of the square root in the denominator.
To rationalize the denominator, you multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of a radical expression involves changing the sign between the terms.
In this case, the conjugate of √2 is -√2. So, multiply both the numerator and denominator by -√2:
(86√2 * -√2) / (√2 * -√2)
Simplifying the numerator and denominator:
= (-86√2 * √2) / (-2)
= (-86 * 2) / (-2)
= -172 / -2
The negative signs in the numerator and denominator cancel each other out:
= 172 / 2
Finally, divide:
= 86
Therefore, the exact answer to divide 86√2 is 86.