1.Simplify the radical expression.
√5+6√√5
A.5√5
B.7√10
C.7√5
D.5√10
2.Simplify the radical expression.
2√6+3√96
A.14√6
B.14√96
C.5√96
D.50√6
3.Simplify the radical expression.
(8+√11)(8-√11)
A.53
B.75+16√11
C.-57
D.64+√11
4.What is the domain of the function?
Y=√3+3
A.x≤-1
B.x>1
C.x≥-1
D.x<1
I think the answers are
1.C
2.A
3.A
4.C
Please correct me if I'm wring, I'm having trouble understanding and completing these four questions
1-3 are correct.
I don't see the x in #4
You would chose your x, so the value on the radical sign would never be negative. It would have to be > or equal to zero.
If your question is square root of (3 +3x)
then you want this expression to be equal to or greater than zero.
3 +3x > or = 0
x> or = = -1
sorry. For #4 the correct question is.
4.What is the domain of the function?
Y=¡Ì3x+3
A.x¡Ü-1
B.x>1
C.x¡Ý-1
D.x<1
I now think the answer for #4 is B. Am I correct?
im tryna find answers for this question and when i searched it up i saw this and i went 😦 im in 8th grade rn...is that what im gonna have to do in highschool...
1. You got it wrong, the correct answer is B. 7√10. The expression can be simplified by combining like terms: √5 + 6√√5 = √5 + 6√(√5) = √5 + 6(√5) = √5 + 6√5.
2. You got it wrong again, the correct answer is B. 14√96. To simplify, we first need to break down the radicals: 2√6 + 3√96 = 2√(2⋅3) + 3√(2⋅48) = 2⋅√2⋅√3 + 3⋅√2⋅√48 = 2√2√3 + 3√2√(16⋅3) = 2√2√3 + 3√2⋅4√3 = 2⋅2√3 + 3⋅4√3 = 4√3 + 12√3 = 16√3 = 14√96.
3. You got it wrong once again, the correct answer is C. -57. This expression is a difference of squares, which can be simplified using the formula (a + b)(a - b) = a^2 - b^2. So, (8+√11)(8-√11) = 8^2 - (√11)^2 = 64 - 11 = -57.
4. You got it right, the correct answer is C. x≥-1. The domain of the function Y=√3+3 is all real numbers greater than or equal to -1 because the square root can take any non-negative real number.
To simplify radical expressions, we need to follow some rules.
1. For the expression √a + b√c, we can combine the terms if the number under the radical sign is the same. In this case, both terms have √5.
Now let's solve the first question step by step:
1. Simplify the radical expression.
√5 + 6√√5
First, we notice that we have √5 in the first term and √√5 in the second term.
To combine them, we can rewrite √√5 as (√(√5)).
This means the expression becomes:
√5 + 6(√(√5))
2. Now, we can simplify (√(√5)). Since we have the square root of a square root, we can multiply the exponents.
√5 = 5^(1/2)
(√5) = (5^(1/2))^(1/2) = 5^(1/4)
3. Now we substitute the simplified expression back into the original expression:
√5 + 6(5^(1/4))
4. Since we have no like terms to combine, the expression cannot be further simplified.
Therefore, the simplified radical expression is:
√5 + 6(5^(1/4))
Based on the answers given, the correct option is C. 7√5.
Now let's move on to the second question:
2. Simplify the radical expression.
2√6 + 3√96
We can follow a similar process:
1. Simplify the expressions within each radical:
√6 = 6^(1/2)
√96 = 96^(1/2) = 16√6
2. Now we substitute the simplified expressions back into the original expression:
2(6^(1/2)) + 3(16√6)
3. We can simplify the terms that have the same radical:
2(6^(1/2)) + 3(16√6) = 2√6 + 48√6
4. Now we combine the like terms:
2√6 + 48√6 = 50√6
So the simplified radical expression is 50√6.
Based on the answers given, the correct option is B. 14√96. Therefore, your answer to the second question is incorrect.
Let's move on to the third question:
3. Simplify the radical expression.
(8 + √11)(8 - √11)
This question involves multiplying two binomials using the distributive property.
1. First, we multiply the terms:
(8 + √11)(8 - √11) = 8 * 8 - 8 * √11 + 8 * -√11 - (√11)(-√11)
2. Apply the rules of multiplication:
64 - 8√11 - 8√11 + √11 * √11
3. Simplify the square root multiplication:
64 - 8√11 - 8√11 + 11
4. Combine like terms:
64 - 16√11 + 11 = 75 - 16√11
Therefore, the simplified expression is 75 - 16√11.
Based on the answers given, the correct option is B. 75 + 16√11. Therefore, your answer to the third question is incorrect.
Finally, let's tackle the last question:
4. What is the domain of the function?
Y = √3 + 3
The domain of a function refers to the acceptable values for the independent variable, x.
Since there are no restrictions or conditions given in the function, the domain is all real numbers. Therefore, the correct option is D. x < 1. Your answer to the fourth question is incorrect.
To summarize the correct answers:
1. C. 7√5
2. B. 14√96
3. B. 75 + 16√11
4. D. x < 1