Multiply and Divide Radicals Quick Check 1 of 51 of 5 Items Question Multiply (7–√) (−2–√) . Give an exact answer.(1 point) Responses 14−−√ s
tart root 14 end root 5–√
start root 5 end root −14−−√
negative start root 14 end root −72–√
To multiply (7–√) and (-2–√), we can use the FOIL method.
(7–√) (−2–√) = 7(-2) + 7(-√) + (-√)(-2) + (-√)(-√)
Simplifying, we get:
= -14 - 7√ - 2√ + √²
Since √² is equal to the square root of 1, we have:
= -14 - 9√ + 1
Combining like terms, we get:
= -13 - 9√
To multiply the radical expressions (7–√) and (-2–√), we need to use the distributive property.
(7–√) * (-2–√) = 7 * (-2) + 7 * (-√) + (-√) * (-2) + (-√) * (-√)
Simplifying further, we get:
-14 - 7√ -2√ + √^2
Since √^2 is just equal to the square root of the number, which is 1, we have:
-14 - 7√ -2√ + 1
Combining like terms, we have:
-14 - 9√ + 1
Simplifying further, we get:
-13 - 9√
So, the exact answer is -13 - 9√.
To multiply the expression (7–√)(−2–√), we can use the distributive property.
Step 1: Multiply the first term in the first parenthesis by both terms in the second parenthesis.
(7)(-2) = -14
(7)(-√) = -7√
Step 2: Multiply the second term in the first parenthesis by both terms in the second parenthesis.
(-√)(-2) = 2√
(-√)(-√) = √ × √ = (√)² = 1
Step 3: Combine the like terms.
-14 - 7√ + 2√ + 1 = -13√ - 13
So, the answer is -13√ - 13.