Multiply (7–√) (−2–√) . Give an exact answer.(1 point)
To simplify the expression (7–√) (−2–√), we can use the distributive property.
(7–√) (−2–√) = 7(-2) + 7(-√) + (-√)(-2) + (-√)(-√)
= -14 - 7√ - 2√ + √(√)
= -14 - 9√ + √(√)
Therefore, the exact answer is -14 - 9√ + √(√).
To multiply (7 - √) by (-2 - √), we can use the distributive property of multiplication over addition/subtraction.
Let's break down the steps to find the product:
Step 1: FOIL Method
First, apply the FOIL (First, Outer, Inner, Last) method to multiply the two binomials. FOIL means multiplying the First terms, then the Outer terms, followed by the Inner terms, and finally the Last terms.
(7 - √) * (-2 - √)
= (7 * -2) + (7 * -√) + (-2 * -√) + (-√ * -√)
Step 2: Simplifying the Expression
Now, let's simplify the expression further:
= -14 - 7√ - 2√ + √²
Since √² equals to the square root of 2 or √2, we can substitute it:
√² = √2
= -14 - 9√ + √2
So the product of (7 - √) and (-2 - √) is -14 - 9√ + √2.
wrong bot
Apologies for the mistake, let me correct it.
To multiply (7 - √) by (-2 - √), we can use the distributive property:
(7 - √) * (-2 - √) = 7 * (-2) + 7 * (-√) + (-√) * (-2) + (-√) * (-√)
= -14 - 7√ + 2√ + √²
Since √² equals to the square root of 2 or √2:
= -14 - 5√ + √2
So the product of (7 - √) and (-2 - √) is -14 - 5√ + √2.
To multiply (7–√) and (−2–√), we can use the FOIL method (First, Outer, Inner, Last):
(7–√) * (−2–√)
First: 7 * -2 = -14
Outer: 7 * -√ = -7√
Inner: -√ * -2 = 2√
Last: -√ * -√ = √^2 = √
Combining these terms, we get:
-14 -7√ + 2√ + √
Simplifying the terms, we have:
-14 -5√ + √
Next, combine like terms:
-14 - 4√
So, the exact answer of (7–√) * (−2–√) is -14 - 4√.
pick one from the answers that I GIVE YOU
√ 14
-√ 15
√ 5
-7√ 2
pick ONE
I apologize for the confusion. The correct answer from the options you provided is:
√ 5
ok next question
divide 86√2 . Provide an exact answer.(1 point)
1.This expression is already simplified and cannot be divided further
2.4√6
3.8√3
4.4√3
pick one answer i gave you here
To divide 86√2, we can simplify the expression further.
86√2 can be written as (86 * 1)√2.
Dividing by a square root is equivalent to multiplying by its conjugate. The conjugate of √2 is also √2.
So, we multiply (86 * 1) by (√2 / √2):
(86 * 1) * (√2 / √2) = 86 * (√2 / √2) = 86 * (1) = 86
Therefore, the exact answer is 86.
The correct answer from the options provided is:
1. This expression is already simplified and cannot be divided further
Divide 410√2√ . Provide an exact answer. (1 point)
1.2√10
2.2√5
3.4√5
4.This expression is already simplified and cannot be divided further
To divide 410√2√, we can simplify the expression further.
410√2√ can be written as (410 * 1)√(2 * √2).
Simplifying the square root of a square root, we have:
√(2 * √2) = √2 * √√2 = √2 * (√2)^(1/2) = √2 * 2^(1/2)
Now, we can rewrite the expression as:
(410 * 1) * (√2 * 2^(1/2))
410 * (√2 * 2^(1/2)) = 410√2 * 2^(1/2)
Since 410 = 2 * 205, we can simplify further:
410√2 * 2^(1/2) = 2 * 205 * √2 * 2^(1/2) = 2 * 205 * √2 * √(2)^(1/2) = 2 * 205 * √2 * 2^(1/4)
Multiplying the coefficients and simplifying the square roots, we have:
2 * 205 * √2 * 2^(1/4) = 410√2 * 2^(1/4)
Therefore, the exact answer is 410√2 * 2^(1/4).
The correct answer from the options provided is:
4. This expression is already simplified and cannot be divided further
Simplify 300−−−√.(1 point)
1.This radical expression is already fully simplified
2.100√3
3.5√12
4.10√3
To simplify √300, we can find the prime factorization of 300.
The prime factorization of 300 is 2^2 * 3 * 5^2.
Now, we can simplify the square root expression:
√300 = √(2^2 * 3 * 5^2) = √(2^2) * √3 * √(5^2) = 2 * √3 * 5 = 10√3.
Therefore, the simplified form of √300 is 10√3.
The correct answer from the options provided is:
4. 10√3.
Simplify 1327−−√ .(1 point)
1.39
2.This radical expression is already fully simplified.
3.16√3
4.39√3
To simplify √1327, we need to find the prime factorization of 1327.
Upon calculating, we find that 1327 is a prime number and cannot be further factored.
Therefore, the simplified form of √1327 is already fully simplified.
The correct answer from the options provided is:
2. This radical expression is already fully simplified.
you gave me a 1/5 bot! your wrong!
Apologies for the incorrect response. Let's properly simplify √1327.
Since 1327 is a prime number, we cannot simplify √1327 any further using exact values. Therefore, the correct answer is:
2. This radical expression is already fully simplified.