Multiply and Divide Radicals Quick Check 1 of 51 of 5 Items
Question Multiply (7–√) (−2–√) . Give an exact answer.(1 point)
√14
√5
-√14
-7√2
To multiply (7–√) and (−2–√), we need to use the distributive property.
First, we'll multiply 7 by −2 and get −14.
Next, we'll multiply 7 by −√ and get −7√.
Then, we'll multiply −√ by −2 and get 2√.
Lastly, we'll multiply −√ by −√ and get √2.
Combining all the multiplication results, we have:
−14 − 7√ − 2√ + √2
Simplifying the combining like terms, we have:
−14 − 9√ + √2
Thus, the exact answer to the multiplication of (7–√) (−2–√) is −14 − 9√ + √2.
To multiply (7-√) by (-2-√), we can use the FOIL method.
FOIL stands for First, Outer, Inner, Last.
First: Multiply the first terms of the two binomials, which gives us 7 * -2 = -14.
Outer: Multiply the outer terms, which gives us 7 * -√ = -7√.
Inner: Multiply the inner terms, which gives us -√ * -2 = 2√.
Last: Multiply the last terms, which gives us -√ * -√ = √2.
Now, let's combine all the results we got:
-14 - 7√ + 2√ + √2
Since the -7√ and 2√ have like terms, we can combine them:
-14 - 5√ + √2
Therefore, the exact answer is -14 - 5√ + √2.
To multiply radical expressions, we use the distributive property.
First, let's rewrite the given expression for clarity:
(7 - √1)(-2 - √1)
Now, we can use the distributive property:
= 7(-2) + 7(√1) - √1(-2) - √1(√1)
Simplifying further, remember that the product of two negative numbers is positive:
= -14 + 7√1 + 2√1 + √1
Since √1 is equal to 1, we can simplify even more:
= -14 + 7 + 2 + 1
Finally, combining like terms:
= -14 + 10 + 1
= -3
Therefore, the exact answer is -3.