Sandra was simplifying 4√5×2√3√
, and she ended up with 8√15−−√
as her simplified answer.
Is Sandra correct? If she is not correct, what was her mistake?
Responses
Sandra's answer is not correct. She should have added the coefficients to get 6 square root of 15.
Sandra's answer is not correct. She could continue to simplify the radical to get 24√5
.
Sandra's answer is not correct. She should have multiplied 4 times 5 in the first radical and multiplied 2 times 3 in the second radical to get a final answer of 26.
Sandra's simplified answer is correct.
Sandra made a mistake in her simplification. The correct answer should be 6√15
You live at point B and your friend lives at point D. You forgot something at your friend's house, and you both agreed to meet in the middle of your two houses. Point B is (-2, 4), Point C is (3, 2), Point D is (1, -1), and Point A is (-4, 1) Which point do you meet at?
(0, 1)
(-0.5, 1.5)
(1.5, -0.5)
(1, 0)
To find the point where you will meet, you need to calculate the average of the x-coordinates and the average of the y-coordinates of your house and your friend's house.
The x-coordinate average is: (-2 + 1) / 2 = -1/2
The y-coordinate average is: (4 + -1) / 2 = 3/2
Therefore, you will meet at the point (-1/2, 3/2), which is equivalent to (-0.5, 1.5).
So, the correct answer is (-0.5, 1.5).
Show all of your steps for how to simplify 3√5×2√10
. Your final answer should be in simplified radical form (not a decimal). Answers only with no work shown will receive no credit.
To simplify 3√5 × 2√10, we can first multiply the coefficients (the numbers outside the radicals) and then multiply the radicands (the numbers inside the radicals).
Step 1: Multiply the coefficients: 3 × 2 = 6.
Step 2: Multiply the radicands: √5 × √10 = √(5 × 10) = √50.
Now, we can simplify √50 further by finding a perfect square factor. Since 50 can be divided evenly by 25, we can rewrite √50 as √(25 × 2).
Step 3: Rewrite √50 as √(25 × 2) = √25 × √2.
Step 4: Simplify √25 = 5.
Putting it all together, we have 6√2 × 5 = 30√2.
Therefore, the simplified radical form of 3√5 × 2√10 is 30√2.
Sandra's answer is not correct. She made a mistake in multiplying the coefficients of the radicals. The correct answer should be 6√15.
Sandra's answer is not correct. To understand her mistake, let's break down the expression she was simplifying: 4√5 × 2√3.
To simplify this expression, we apply the multiplication rule for radicals, which states that the product of two radicals with the same index can be expressed as a single radical with the product of their radicands, multiplied by the product of their coefficients.
So, in this case, we first multiply the coefficients 4 and 2 to get 8. Then, we multiply the radicands 5 and 3 to get 15. Therefore, the simplified expression is 8√15.
But Sandra's answer was 8√15−−√, which is not correct. The correct answer would be 8√15.
Therefore, Sandra made a mistake when subtracting the radical symbol instead of simplifying the answer correctly.