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Question 1 of 4
Express the following with rational denominators:
12+√212+√2
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For the answer to be in simplest form, the denominator should be a rational number.
Multiply the numerator and the denominator by the conjugate of the denominator which is: 2-√22−√2
| 12+√212+√2 |
== |
12+√2×2-√22-√212+√2×2−√22−√2 |
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2-√2(2+√2)(2-√2)2−√2(2+√2)(2−√2) |
Simplify using the difference of two squares |
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== |
2-√2(2)2-(√2)22−√2(2)2−(√2)2 |
Simplify |
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== |
2-√24-22−√24−2 |
(2)2=4(2)2=4 and (√2)2=2(√2)2=2 |
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== |
2-√222−√22 |
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Question 2 of 4
Express the following with rational denominators:
1√6-√51√6−√5
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For the answer to be in simplest form, the denominator should be a rational number.
Multiply the numerator and the denominator by the conjugate of the denominator which is: √6+√5√6+√5
| 1√6-√51√6−√5 |
== |
1√6-√5×√6+√5√6+√51√6−√5×√6+√5√6+√5 |
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= |
√6+√5(√6-√5)(√6+√5) |
Simplify using the difference of two squares |
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= |
√6+√5(√6)2-(√5)2 |
Simplify square roots |
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√6+√56-5 |
(√36)2=6 and (√25)2=5 |
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= |
√6+√51 |
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= |
√6+√5 |
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Question 3 of 4
Express the following with rational denominators:
44-√2
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For the answer to be in simplest form, the denominator should be a rational number.
Multiply the numerator and the denominator by the conjugate of the denominator which is: 4+√2
| 44-√2 |
= |
44-√2×4+√24+√2 |
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4×4+4√2(4-√2)(4+√2) |
Simplify using the difference of two squares |
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= |
16+4√242-(√2)2 |
Simplify square roots |
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= |
16+4√216-2 |
42=16 and (√2)2=2 |
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= |
16÷2+4√2÷214÷2 |
Simplify by dividing throughout by 2 |
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= |
8+2√27 |
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Question 4 of 4
Express the following with rational denominators:
12√7-√3
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For the answer to be in simplest form, the denominator should be a rational number.
Multiply the numerator and the denominator by the conjugate of the denominator which is: √7+√3
| 12√7-√3 |
= |
12√7-√3×√7+√3√7+√3 |
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= |
12(√7+√3)(√7-√3)(√7+√3) |
Simplify using the difference of two squares |
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= |
12(√7+√3)(√7)2-(√3)2 |
Simplify square roots |
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= |
12(√7+√3)7-3 |
(√7)2=7 and (√3)2=3 |
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= |
12(√7+√3)4 |
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4÷12(√7+√3)4÷4 |
Divide top and bottom by 4 |
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= |
3(√7+√3)class{pk-strike}{4÷4) |
Apply the distributive property |
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3√7+3√3 |
