Arseniy O.
asked • 05/29/17Simplify Expressions in Radicals
A. √(11−6√(2))
B. √(10+4√(6))
C. √(29−12√(5))
D. √(8+2√(15))
I have no idea how to solve these problems, so if you show work that would be greatly appreciated!
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2 Answers By Expert Tutors
Kemal G. answered • 05/29/17
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Patient and Knowledgeable Math and Science Tutor with PhD
Disregard this please.
Kemal G.
C. √(29−12√(5)) = √(3 - 2√5)2
= (3 - 2√5)
D. √(8+2√(15)) = √(√5 + √3)2
= (√5 + √3)
Report
05/29/17
(a-b)2 = a2-2ab+b2.
A. Try to express 11 - 6√2 in the form (a-b)2.
11 - 6√2 = 9 - 2(3)√2 + 2
= (3)2 - 2(3)(√2) + (√2)2 = (3 - √2)2
So, √(11-6√2) = √(3-√2)2 = 3 - √2
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B. Try to express 10+4√6 in the form (a+b)2.
10+4√6 = 4 + 4√6 + 6
= (2)2 + 2(2)√6 + (√6)2
= (2+√6)2
So, √(10+4√6) = √(2+√6)2 = 2+√6
Kemal G.
C. Try to write it in the form of (a - b)2
After some trial and error, I figured out that 3 and 2√5 will work.
(3 - 2√5)2 = 9 - 12√5 + 20
= 29 - 12√5
√(29−12√(5)) = (3 - 2√5)2
D. This is similar to the solution of B.
Try to write it in the form of (a + b)2
√(8+2√(15)) = √(√3 + √5)2
= (√3 + √5)2
(8+2√(15)) = (√3 + √5)2
Report
05/29/17
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Michael J.
05/29/17