What is the simplified form of √48°n?
The simplified form of √48°n is 4√3n.
Is there a degree symbol in 4√3n?
Apologies for the confusion in my previous response. The correct simplified form is √48n, which simplifies to 4√3n. There is no degree symbol in this expression. Thank you for pointing that out.
The answers are,
A: 4n^3√3
B: 4n^4√3n
C: 3n√4n^8
D: 4√3n^9
The correct simplified form of √48°n is D: 4√3n^9. Thank you for providing the correct options.
What is the simplified form of 3√5c x √15c^3?
A: 15c^2√3
B: 6c^2√5
C: 5c^2√3
D: 12c^4√5
To simplify the expression 3√5c * √15c^3, we can multiply the coefficients and combine the square roots:
3 * √5c * √15c^3
= 3 * √(5 * 15 * c * c^3)
= 3 * √(75c^4)
= 3 * √(25 * 3 * c^4)
= 3 * √(25) * √(3) * √(c^4)
= 3 * 5 * √(3) * c^2
= 15c^2√3
Therefore, the simplified form of 3√5c * √15c^3 is A: 15c^2√3.
Which radical expression is in simplified form?
A: 11y/(√3)
B: (√6)/5y
C: √17/√4
D: √25/81
To determine which radical expression is in simplified form, we need to simplify each option:
A: 11y/(√3) = (11y√3)/(√3*√3) = 11y√3/3 = (11√3y)/3
B: (√6)/5y is already simplified, as the square root cannot be simplified further.
C: √17/√4 = √17/2 = (1/2)√17
D: √25/81 = 5/9
Among the options provided, Option B: (√6)/5y is in simplified form.
A gardener is mowing a 20 by 40 yard rectangular pasture using a diagonal pattern. He mows from one corner of the pasture to the corner diagonally opposite. What is the length of this pass with the mower? Give your answer in simplified form. Recall from the Pythagorean Theorem that, for a right triangle, the square of the length of the diagonal is equal to the sum of the squares of the lengths of the sides. (1 point)
To find the length of the diagonal pass, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the sides of the rectangular pasture are 20 yards and 40 yards. Let's call the length of the diagonal pass "d." According to the Pythagorean theorem:
d^2 = 20^2 + 40^2
d^2 = 400 + 1600
d^2 = 2000
To simplify, we can express 2000 as a product of perfect squares:
2000 = 100 * 20 = 10^2 * 20
Therefore, the length of the diagonal pass with the mower is sqrt(2000) = sqrt(10^2 * 20) = 10√20 yards. This is the simplified form of the length of the pass with the mower.